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