Answer:
x = 4 or x = -6
Explanation:
Recall that to solve a quadratic equation by taking the square root of each side, you must follow this pattern:
The solutions of the quadratic equation
X² = k
are
X = ±√k
where X is an expression containing a variable, and k is a number.
Let's look at the problem in this post and put in the form above.
2(x + 1)² + 5 = 55
We need the square of an expression equaling a number, so we solve for (x + 1)².
2(x + 1)² + 5 = 55
Subtract 5 from both sides.
2(x + 1)² = 50
Divide both sides by 2.
(x + 1)² = 25
Now we have the square of an expression on the left side and a number on the right side.
We take the square root of both sides and apply the ± sign to the right side.
x + 1 = ±√25
x + 1 = ±5
x + 1 = 5 or x + 1 = -5
x = 4 or x = -6