-x^2+14x+14=0

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


Simplifying
-1x2 + 14x + 14 = 0

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

Solving
14 + 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'.
-14 + -14x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 14 + 49

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

Combine like terms: 14 + 49 = 63
49 + -14x + x2 = 63

Factor a perfect square on the left side:
(x + -7)(x + -7) = 63

Calculate the square root of the right side: 7.937253933

Break this problem into two subproblems by setting 
(x + -7) equal to 7.937253933 and -7.937253933.


Subproblem 1
x + -7 = 7.937253933

Simplifying
x + -7 = 7.937253933

Reorder the terms:
-7 + x = 7.937253933

Solving
-7 + x = 7.937253933

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 = 7.937253933 + 7

Combine like terms: -7 + 7 = 0
0 + x = 7.937253933 + 7
x = 7.937253933 + 7

Combine like terms: 7.937253933 + 7 = 14.937253933
x = 14.937253933

Simplifying
x = 14.937253933


Subproblem 2
x + -7 = -7.937253933

Simplifying
x + -7 = -7.937253933

Reorder the terms:
-7 + x = -7.937253933

Solving
-7 + x = -7.937253933

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 = -7.937253933 + 7

Combine like terms: -7 + 7 = 0
0 + x = -7.937253933 + 7
x = -7.937253933 + 7

Combine like terms: -7.937253933 + 7 = -0.937253933
x = -0.937253933

Simplifying
x = -0.937253933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.937253933, -0.937253933}

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