Question

Complete the square to solve the following quadratic equation: x^2+2x−8=0 .

Answer 1

To complete the square, we need to take half of the coefficient of x (which is 2) and square it.

Half of 2 is 1, and 1 squared is 1.

To complete the square, we need to add 1 to both sides of the equation:

x^2 + 2x − 8 + 1 = 0 + 1

This simplifies to:

x^2 + 2x - 7 = 0

The left side of the equation can be factored as:

(x + 4)(x - 2) = 0

Setting each factor equal to zero, we can solve for x:

x + 4 = 0, x - 2 = 0

x = -4, x = 2

So the solutions to the quadratic equation x^2 + 2x - 8 = 0 are x = -4 and x = 2.