How do you solve the quadratic equation by completing the square: x^2 + 4x = 21x2+4x=21?

1 Answer
Stefan V.
Aug 12, 2015

x_(1,2) = -2 +- 5x1,2=−2±5

Explanation:

To solve this quadratic by completing the square, you need to use the coefficient of the xx-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 xx-term by 22, the nsquare the result

(4/2)^2 = 2^2 = 4(42)2=22=4

Add this term to both sides of the equation to get

x^2 + 4x + 4 = 21 + 4x2+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)^2x2+4x+4=x2+2⋅(2)⋅x+(2)2=(x+2)2

This means that you now have

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

Take the square root of both sides

sqrt((x+2)^2) = sqrt(25)√(x+2)2=√25

x+2 = +- 5x+2=±5

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

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