Tuesday, May 25, 2010

Quadratic Equation: Completing the Square

One way of solving for x in a quadratic equation is by completing the square. Here's how:

x^2 + 6x - 7 = 0 ===> ax^2 +bx + c = 0
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1) Move the constant to the right side. In the equation above, the constant is 7. You can do this by adding the negative value of the constant on both sides of the equation;

x^2 + 6x -7 + (+7) = 0 + (+7)

x^2 + 6x = 7

2) Take half the value of the x-term or b ( 6).

6/2 = 3

3) Square it.

3^2 = 9

4) Add the result to both sides.

x^2 + 6x + 9 = 7 + 9

5) Convert the left side to squared form and simplify the right side.

( x + 3)^2 = 16

6) Take the square root of both sides.

x + 3 = +/- 4

7) Solve for x

x + 3 = 4
x = 4 - 3
x = 1
========
x + 3 = -4
x = -4 - 3
x = -7
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Answers:
x = 1 and -7

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