-x^2+14x+40=0

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Solution for -x^2+14x+40=0 equation: 


Simplifying
-1x2 + 14x + 40 = 0

Reorder the terms:
40 + 14x + -1x2 = 0

Solving
40 + 14x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-40 + -14x + x2 = 0

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -14x + 40 + x2 = 0 + 40

Reorder the terms:
-40 + 40 + -14x + x2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -14x + x2 = 0 + 40
-14x + x2 = 0 + 40

Combine like terms: 0 + 40 = 40
-14x + x2 = 40

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 40 + 49

Reorder the terms:
49 + -14x + x2 = 40 + 49

Combine like terms: 40 + 49 = 89
49 + -14x + x2 = 89

Factor a perfect square on the left side:
(x + -7)(x + -7) = 89

Calculate the square root of the right side: 9.433981132

Break this problem into two subproblems by setting 
(x + -7) equal to 9.433981132 and -9.433981132.


Subproblem 1
x + -7 = 9.433981132

Simplifying
x + -7 = 9.433981132

Reorder the terms:
-7 + x = 9.433981132

Solving
-7 + x = 9.433981132

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 9.433981132 + 7

Combine like terms: -7 + 7 = 0
0 + x = 9.433981132 + 7
x = 9.433981132 + 7

Combine like terms: 9.433981132 + 7 = 16.433981132
x = 16.433981132

Simplifying
x = 16.433981132


Subproblem 2
x + -7 = -9.433981132

Simplifying
x + -7 = -9.433981132

Reorder the terms:
-7 + x = -9.433981132

Solving
-7 + x = -9.433981132

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -9.433981132 + 7

Combine like terms: -7 + 7 = 0
0 + x = -9.433981132 + 7
x = -9.433981132 + 7

Combine like terms: -9.433981132 + 7 = -2.433981132
x = -2.433981132

Simplifying
x = -2.433981132


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.433981132, -2.433981132}

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