How do you solve the quadratic equation by completing the square: #x^2 + 4x = 21#?

1 Answer
Aug 12, 2015

Answer:

#x_(1,2) = -2 +- 5#

Explanation:

To solve this quadratic by completing the square, you need to use the coefficient of the #x#-term to help you find a number that when added to both sides of the equation will allow you to write the left side as the square of a binomial.

More specifically, you need to divide the coefficient of the #x#-term by #2#, the nsquare the result

#(4/2)^2 = 2^2 = 4#

Add this term to both sides of the equation to get

#x^2 + 4x + 4 = 21 + 4#

Now, the left side of the equaation can be written as

#x^2 + 4x + 4 = x^2 + 2 * (2) * x + (2)^2 = (x+2)^2#

This means that you now have

#(x+2)^2 = 25#

Take the square root of both sides

#sqrt((x+2)^2) = sqrt(25)#

#x+2 = +- 5#

#x = -2 +- 5 = {(x_1 = -2-5 = -7), (x_2 = -2 + 5 = 3) :}#