Answer:
x = 2
x = -4
Explanation:
When trying to solve a quadratic equation using completing the square method, we try to get the LHS of the equation in the form of the square of an expression
A quadratic equation is of the form ax² + bx = c where a, b and c are constants
Here original equation is x² + 2x = 8
a = 1, b = 2 and c=8
Take half the coefficient of x ie b, square it and add it to both sides
(b/2)² = (2/2)² = 1² = 1
Adding 1 to both sides, we get
x² + 2x + 1 = 8 + 1
x² + 2x + 1 = 9
Using the fact that (a+b)² = a² + 2ab + b² we can see that
x² + 2x + 1 = (x+1)² (See note below)
So we get
(x+1)² = 9
Taking square roots on both sides
x + 1 = ±√9
x + 1 = ±3
So x+1 = 3 ==> x = -1 +3 = 2
x+1 = -3 ==> -1-3=--4
So the solutions are x=2 and x = -4
Note
(x+1)² = x² + 2.1.x + 1² = x² + 2x + 1