Question

Solve the following quadratic equation for all values of x.
2(х + 1)^2 - 35 = 15

Answer 1

Starting with the equation:

2(x + 1)^2 - 35 = 15

First, we can simplify by adding 35 to both sides:

2(x + 1)^2 = 50

Then we can divide both sides by 2:

(x + 1)^2 = 25

Taking the square root of both sides, we get:

x + 1 = ±5

Now we can solve for x by subtracting 1 from both sides:

x = -1 ± 5

This gives us two possible values for x:

x = -1 + 5 = 4

or

x = -1 - 5 = -6

Therefore, the solutions to the quadratic equation 2(x + 1)^2 - 35 = 15 are x = 4 and x = -6

Answer 2

x = 4 and x = -6

Explanation:

To solve the quadratic equation 2(x + 1)^2 - 35 = 15, we can start by simplifying the left-hand side:

2(x + 1)^2 - 35 = 15

2(x + 1)^2 = 50

(x + 1)^2 = 25

Taking the square root of both sides, we get:

x + 1 = ±5

Solving for x, we get:

x + 1 = 5 or x + 1 = -5

x = 4 or x = -6

Therefore, the solutions to the quadratic equation 2(x + 1)^2 - 35 = 15 are x = 4 and x = -6.