40=-x^2+36x+-87

Solution for 40=-x^2+36x+-87 equation:

Simplifying
40 = -1x2 + 36x + -87

Reorder the terms:
40 = -87 + 36x + -1x2

Solving
40 = -87 + 36x + -1x2

Solving for variable 'x'.

Combine like terms: 40 + 87 = 127
127 + -36x + x2 = -87 + 36x + -1x2 + 87 + -36x + x2

Reorder the terms:
127 + -36x + x2 = -87 + 87 + 36x + -36x + -1x2 + x2

Combine like terms: -87 + 87 = 0
127 + -36x + x2 = 0 + 36x + -36x + -1x2 + x2
127 + -36x + x2 = 36x + -36x + -1x2 + x2

Combine like terms: 36x + -36x = 0
127 + -36x + x2 = 0 + -1x2 + x2
127 + -36x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
127 + -36x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-127' to each side of the equation.
127 + -36x + -127 + x2 = 0 + -127

Reorder the terms:
127 + -127 + -36x + x2 = 0 + -127

Combine like terms: 127 + -127 = 0
0 + -36x + x2 = 0 + -127
-36x + x2 = 0 + -127

Combine like terms: 0 + -127 = -127
-36x + x2 = -127

The x term is -36x.  Take half its coefficient (-18).
Square it (324) and add it to both sides.

Add '324' to each side of the equation.
-36x + 324 + x2 = -127 + 324

Reorder the terms:
324 + -36x + x2 = -127 + 324

Combine like terms: -127 + 324 = 197
324 + -36x + x2 = 197

Factor a perfect square on the left side:
(x + -18)(x + -18) = 197

Calculate the square root of the right side: 14.035668848

Break this problem into two subproblems by setting 
(x + -18) equal to 14.035668848 and -14.035668848.

Subproblem 1
x + -18 = 14.035668848

Simplifying
x + -18 = 14.035668848

Reorder the terms:
-18 + x = 14.035668848

Solving
-18 + x = 14.035668848

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = 14.035668848 + 18

Combine like terms: -18 + 18 = 0
0 + x = 14.035668848 + 18
x = 14.035668848 + 18

Combine like terms: 14.035668848 + 18 = 32.035668848
x = 32.035668848

Simplifying
x = 32.035668848

Subproblem 2
x + -18 = -14.035668848

Simplifying
x + -18 = -14.035668848

Reorder the terms:
-18 + x = -14.035668848

Solving
-18 + x = -14.035668848

Solving for variable 'x'.

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

Add '18' to each side of the equation.
-18 + 18 + x = -14.035668848 + 18

Combine like terms: -18 + 18 = 0
0 + x = -14.035668848 + 18
x = -14.035668848 + 18

Combine like terms: -14.035668848 + 18 = 3.964331152
x = 3.964331152

Simplifying
x = 3.964331152

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.035668848, 3.964331152}