Question

Use completing the square to solve the equation x2+10x=−5.x2+10x=-5. first determine the number you must add to both sides of the equation.

Answer 1

x^2 + 10x = - 5

To complete the square, we need to add a constant on the left side that makes the expression on the right a perfect square trinomial. We need to add the same value on the right side to keep the equation equal. So,

x^2 + 10x + a = -5 + a

where a is the square of one-half the coefficient of x, therefore:

a = (10 / 2)^2 = 25

x^2 + 10x + 25 = -5 + 25

(x + 5)^2 = 20

Taking the square root of both sides:

x + 5 = ± 4.47

x = -5 ± 4.47

x = -9.47, -0.53