x+(x+1)+x^2=64

Solution for x+(x+1)+x^2=64 equation:

Simplifying
x + (x + 1) + x2 = 64

Reorder the terms:
x + (1 + x) + x2 = 64

Remove parenthesis around (1 + x)
x + 1 + x + x2 = 64

Reorder the terms:
1 + x + x + x2 = 64

Combine like terms: x + x = 2x
1 + 2x + x2 = 64

Solving
1 + 2x + x2 = 64

Solving for variable 'x'.

Reorder the terms:
1 + -64 + 2x + x2 = 64 + -64

Combine like terms: 1 + -64 = -63
-63 + 2x + x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-63 + 2x + x2 = 0

Factor a trinomial.
(-9 + -1x)(7 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-9, 7}