Math Algebra
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Math Algebra

by Jollibee Tampos
(Davao City)

solution of a quadratic by factoring

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Math Algebra

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Jul 30, 2011
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Math Algebra - Quadratic
by: Staff


The question:

by Jollibee Tampos
(Davao City)


solution of a quadratic by factoring


The answer:


Here is an example of a quadratic equation which can be solved by factoring:

2x² - 5x - 3 = 0

Factor the left side of the equation:

(2x + 1)(x - 3) = 0


The question at this point is “what now”?


There are two solutions:

(2x + 1)(x - 3) = 0


1st solution:

“Divide” each side of the equation “by (x - 3)”, and then solve for x

(2x + 1)(x - 3)/(x - 3) = 0/(x - 3)

(2x + 1)*[(x - 3)/(x - 3)] = 0/(x - 3)

(2x - 1)*1 = 0/(x - 3)

(2x + 1) = 0/(x - 3)

2x + 1 = 0/(x - 3)

2x + 1 = 0

2x + 1 - 1 = 0 - 1

2x + 0 = 0 - 1

2x = 0 - 1

2x = -1

2x/2 = -1/2

x * (2/2) = -½

x * 1 = -1/2

x = -1/2


2nd solution:

“Divide” each side of the equation “by (2x + 1)”, and then solve for x

(2x + 1)(x - 3)/( 2x + 1) = 0/(2x + 1)

(x - 3)*[( 2x + 1)/( 2x + 1)] = 0/(2x + 1)

(x - 3)*1 = 0/(2x + 1)

(x - 3) = 0/(2x + 1)

x - 3 = 0/(2x + 1)

x - 3 = 0

x - 3 + 3 = 0 + 3

x + 0 = 0 + 3

x = 0 + 3

x = 3


check the solution by substituting the two numerical values of x into the original equation:

1st solution, x = -½

2x² - 5x - 3 = 0

2(-½)² - 5(-½) - 3 = 0

2(1/4) - 5(-½) - 3 = 0

2/4 + 5(½) - 3 = 0

1/2 + 5(½) - 3 = 0
0.5 + 2.5 - 3 = 0

0 = 0, OK


2nd solution, x = 3

2x² - 5x - 3 = 0

2(3)² - 5(3) - 3 = 0

2(9) - 5(3) - 3 = 0

18 - 5(3) - 3 = 0

18 - 15 - 3 = 0

0 = 0, OK



Thanks for writing.

Staff
www.solving-math-problems.com



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