ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Solving a Quadratic Equation by Using the Quadratic Formula

Updated on September 3, 2015

Do you know the Quadratic Formula?

See results

The origins of the Quadratic Formula

Sometime in the annals of history someone realized that they were solving quadratic equations by completing the square – each time the method was identical and thus using algebra they managed to create a formula that could be used instead of the individual steps.

The formula above is the result and it is one of the most used formulas in mathematics. The quadratic formula will always produce an answer (even if there are imaginary numbers involved) and helps solves equations that cannot use other methods such as factorization.

Example of Quadratic Formula being Used

The idea of the quadratic formula is to isolate the unknown variable (in this case X) and perform calculations on the known constants (A, B and C). The process is identical every time and as long as you remember the quadratic formula you will be able to solve any quadratic equation especially when other methods fail. Once used often you'll find the quadratic formula will be the easiest to utilize.

X2 – 10X – 24 = 0

Comparing this to the formula aX2 + bX + C = 0 we get a=1, b=-10 and C=-24.

Inserting these values into the quadratic formular we get:

If you insert both values in the original formula you will see that both are valid and solve the equations. While both are valid answers, in this case as we were calculating the dimensions of a lawn then the only valid answer will be x = 12 as a lenth cannot be less than zero.

Potential Problems with the Quadratic Formula.

One of the perceived problems with the quadratic formula is that the equation within the ‘Square Root’ could be negative – in normal mathematics we cannot calculate the square root of a negative number.

However, this is where the concept of i comes in. i is an imaginary number and is defined as the square root of -1. Thus when evaluation the Quadratic Formula you will be able to come up a solution that may sometimes be evaluated as an imaginary number but when this number is inserted into the original equation it produces the desired result.

Tips for using the Quadratic Formula

  • Always get the expression in the format aX2 + bX + C = 0; if you don’t make the formula equal zero, the calculation will fail.
  • Double check your results by inserting them back into the original quadratic equation.
  • Use standard rules to evaluate the quadratic formula. BODMAS or PEMDAS are instructions on the order in which you should evaluate a formula (Brackets, Of, Divide, Multiply, Add, Subtract) or (Parenthesis, Exponents, Multiply, Divide, Add, Subtract).
  • Don’t Panic! – probably the most important advice – the quadratic equation may seem complicated but it is very easy to use and will give the correct solution every time.

Comments

    0 of 8192 characters used
    Post Comment

    • Silver Poet profile image

      Silver Poet 5 years ago from the computer of a midwestern American writer

      I love this sort of math. Thank you for writing this hub to help share the love of algebraic concepts.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: "https://hubpages.com/privacy-policy#gdpr"

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)