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

1 Answer
Aug 1, 2015

Answer:

#x_(1,2) = -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 #x#-term by 2 and square the result.

#6/2 = 3#, then #3^2 = 9#

Add #9# to both sides of the equation to get

#x^2 + 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)#

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

This will get you

#(x+3)^2 = 16#

Take the square root from both sides of the equation

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

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