Answer:
x = -12.42 or x = 2.42
Explanation:
x^2 + 10x - 13 = 17
To solve this using the completing the square method, we will follow the steps below;
First, we will add 13 to both side of the equation, we want only the x variable to be on the left-hand side of the equation
x^2 + 10x - 13 + 13 = 17 + 13
x^2 + 10x = 30
The next step is to add both-side of the equation by square of half of the coefficient of x (that is ; half of 10 is 5, then we will add 5² to both-side of the equation)
x^2 + 10x + 5² = 30 + 5²
Then we can now factorize the left-hand side of the equation and at the same time simplify the right-hand side of the equation
(x + 5)² = 30 + 25
(x + 5)² = 55
We will then take the square root of both-side of the equation
√(x + 5)² = ±√55
x + 5 = ±√55
To get the value of x, we will subtract 5 from both-side of the equation
x + 5 - 5 = ±√55 - 5
x = ±√55 - 5
Either x = + √55 -5 = 7.42 -5 = 2.42
OR
x = -√55 - 5 = -7.42 - 5 = -12.42
Therefore either x = -12.42 or x = 2.42
x = -12.42 or 2.42