# Solving Quadratic Equations By Using Quadratic Formula

Updated on November 30, 2011

Solving Quadratic Equations By Using Quadratic Formula

Quadratic equations is one of the most important concept in Algebra. It is of great importance to gain skill in solving quadratic equations. As a general rule, we may solve a quadratic equation most simply and quickly if we first try to factor the equation. If it cannot be readily factored using quadratic formula is the next best way. The formula works not only for integers a, b and c but for any real number. It works even if the coefficients are complex numbers.

The solutions for the quadratic equation aX^2 + bX + c = 0 are :

X = ( -b +- SQRT( b^2 - 4ac) ) /2a

Example One : Solve the equation 30X^2 + 49X + 20 = 0

To solve this equation we first identify a = 30 b = 49 c = 20

Then substitute the corresponding values in the formula :

X = (-49 +- SQRT ( 49^2 - 4 (30) (20) ))/2(30)

X = ( -49 += SQRT ( 2401 -2400) )/60

X 1 = ( -49 + 1)/60 = -48/60 = -4/5

X2 = ( -49 -1)/60 = -50/60 = -5/6

Example Two :

25X ^2 - 30X + 13 = 0

a = 25 b = -30 c = 13

X = ( 30 +- SQRT ( 30^2 - 4 (25) (13) ) )/2(25)

X = (30 +- SQRT(900 – 1300))/50

X = ( 30 += SQRT (-400))/50

X = (30 += 20i)/50

X1 = (30 + 20i)/50 = 10 (3 + 2i )/50 = (3 + 2i )/5

X2 = ( 30 - 20i )/50 = !0 (3 – 2i )/50 = ( 3 – 2i)/5

Example Number Three :

Solve for the equation X^2 + 4iX - 5 = 0

a = 1 b = 4i c = -5

X = ( -4i +- SQRT( (4i)^2 - 4 (1 ) (-5)) )/(2)(1)

X = ( -4i +- SQRT( -16 + 20))/2 since i^2 = -1

X = ( -4i +- 2)/2

X1 = ( -4i + 2)/2 = 2(-2i + 1)/2 = -2i + 1

X2 = (-4i - 2)/2 = 2(-2i – 1 )/2 = -2i - 1

SOURCE: COLLEGE ALGEBRA By :

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• Justin W Price

7 years ago from Juneau, Alaska

thank you!

• Justin W Price

7 years ago from Juneau, Alaska

thank you!

• AUTHOR

Maria Cristina Aquino Santander

7 years ago from Manila

Hi PDXKaraokeGuy thank you for dropping by. Your visit is much appreciated. Blessings to you and best regards.

• Justin W Price

7 years ago from Juneau, Alaska

thanks for this hub. I'm taking my last algebra class and I have a final in two weeks. I'll be referring to this later!

• AUTHOR

Maria Cristina Aquino Santander

7 years ago from Manila

Hi carcro great to hear from you again. Thank you for appreciating this hub. Your visit is much appreciated. Blessings to you always. Best regards.

• Paul Cronin

7 years ago from Winnipeg

You are definitely a math expert. I always enjoyed math as a kid and still get to tutor my kids along when necessary. great info here, voted up!

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