Put the equation in the form ax2 + bx + c = 0. Enter exponents using the caret ( ^ ). For example, you would enter 4x2 as 4x^2.

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To put the equation in the form ax^2 + bx + c = 0, let's simplify and rearrange the given equation step by step.

Given equation: 8 - 2x^2 = (x + 2)^2 - 7

To start with, let's expand the square on the right side of the equation:

8 - 2x^2 = (x + 2)(x + 2) - 7

Using the FOIL method to multiply (x + 2)(x + 2), we get:

8 - 2x^2 = (x^2 + 2x + 2x + 4) - 7

Combining like terms, we have:

8 - 2x^2 = (x^2 + 4x + 4) - 7

Now, let's simplify further by distributing the negative sign into the parentheses:

8 - 2x^2 = x^2 + 4x + 4 - 7

Combining like terms again, we get:

8 - 2x^2 = x^2 + 4x - 3

To put the equation in standard form, we need to move all terms to one side of the equation. So, let's subtract (8 - 2x^2) from both sides:

0 = x^2 + 4x - 3 - (8 - 2x^2)

Simplifying this further, we have:

0 = x^2 + 4x - 3 - 8 + 2x^2

Combining like terms once again, we get:

0 = 3x^2 + 4x - 11

Finally, the equation is now in the form ax^2 + bx + c = 0, where a = 3, b = 4, and c = -11:

3x^2 + 4x - 11 = 0