How do you solve the quadratic equation by completing the square: x^2+6x=7x2+6x=7?

1 Answer
Stefan V.
Aug 1, 2015

x_(1,2) = -3 +- 4x1,2=−3±4

Explanation:

In order to solve this quadratic equation by completing the square, you need to write the left side of the equation as the square of a binomial.

To do that, you need to add a term to both sides of the equaion. More specifically, you need to divide the coefficient of xx-term by 2 and square the result.

6/2 = 362=3, then 3^2 = 932=9

Add 99 to both sides of the equation to get

x^2 + 6x + 9 = 7 + 9x2+6x+9=7+9

The left side of the equation can now be written as

x^2 + 6x + 9 = x^2 + 2 * (3) * x + (3^2)x2+6x+9=x2+2⋅(3)⋅x+(32)

x^2 + 6x + 9 = (x + 3)^2x2+6x+9=(x+3)2

This will get you

(x+3)^2 = 16(x+3)2=16

Take the square root from both sides of the equation

sqrt((x+3)^2) = sqrt(16)√(x+3)2=√16

x+3 = +- 4 => x_(1,2) = -3 +- 4 = {(x_1 = -3-4 = color(green)(-7)), (x_2 = -3 + 4 = color(green)(1)) :}

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