Answer: To solve the quadratic equation x^2 + 10x - 8 = 0 by completing the square, we want to convert the equation into the form (x + p)^2 = q. To do this, we need to add a specific value to both sides of the equation.
The value that should be added to both sides of the equation is (b/2)^2, where b is the coefficient of the linear term (in this case, 10x).
Step 1: Identify the coefficient of the linear term (b).
b = 10
Step 2: Find (b/2)^2.
(b/2)^2 = (10/2)^2 = 5^2 = 25
Step 3: Add (b/2)^2 to both sides of the equation.
x^2 + 10x - 8 + 25 = 0 + 25
x^2 + 10x + 17 = 25
Now, we have the quadratic equation in the form (x + p)^2 = q. To complete the square, we need to solve for x + p:
x + p = ±√q
x + p = ±√25
x + p = ±5
Step 4: Solve for x:
x = -p ± 5
Now, we need to find the value of p. To do this, we look at the coefficient of the x term in the original equation (10x) and divide it by 2:
p = 10/2 = 5
Step 5: Substitute the value of p into the solution for x:
x = -5 ± 5
Now, we have two possible solutions for x:
x = -5 + 5 = 0
x = -5 - 5 = -10
So, the two solutions to the quadratic equation x^2 + 10x - 8 = 0 are x = 0 and x = -10.