Final answer:
To complete the square for the equation x²+8x-5=15, we form a perfect square trinomial, take the square root of both sides, and solve for x to get the solutions x = 2 and x = -10.
Step-by-step explanation:
To complete the square and solve the equation x²+8x-5=15, we first move all terms to one side of the equation to set it equal to zero:
x²+8x-5-15=0 → x²+8x-20=0
Now, we need to form a perfect square trinomial from the quadratic and linear terms. To do this, we add and subtract the square of half the coefficient of x, which is (8/2)²=16, inside the equation:
x²+8x+16-16-20=0
x²+8x+16=36
(x+4)² = 36
Next, we take the square root of both sides of the equation:
√(x+4)² = ±√36
x+4 = ± 6
So, the two possible solutions for x are:
x = -4+6 or x = -4-6
x = 2 or x = -10
Therefore, the solutions are x = 2 and x = -10.