(x+1)² = 7918 - 2x (x+2)² = 3131 - 2x

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To solve these equations, we need to expand and simplify the expressions on both sides.

Expanding the first equation:
(x+1)² = (x+1)(x+1)
= x² + x + x + 1
= x² + 2x + 1

So, the first equation becomes:
x² + 2x + 1 = 7918 - 2x

Expanding the second equation:
(x+2)² = (x+2)(x+2)
= x² + 2x + 2x + 4
= x² + 4x + 4

So, the second equation becomes:
x² + 4x + 4 = 3131 - 2x

Now we have two equations:

x² + 2x + 1 = 7918 - 2xx² + 4x + 4 = 3131 - 2x

We can simplify these equations further by combining like terms:

x² + 4x + 7917 = 0x² + 6x + 3127 = 0

Now these are two quadratic equations that we can solve using methods like factoring, completing the square, or the quadratic formula. Let me know if you'd like me to solve them for you using a specific method.