-x^2+14x-9=0

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Solution for -x^2+14x-9=0 equation: 


Simplifying
-1x2 + 14x + -9 = 0

Reorder the terms:
-9 + 14x + -1x2 = 0

Solving
-9 + 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'.
9 + -14x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -14x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -14x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -14x + x2 = 0 + -9
-14x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-14x + x2 = -9

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 = -9 + 49

Reorder the terms:
49 + -14x + x2 = -9 + 49

Combine like terms: -9 + 49 = 40
49 + -14x + x2 = 40

Factor a perfect square on the left side:
(x + -7)(x + -7) = 40

Calculate the square root of the right side: 6.32455532

Break this problem into two subproblems by setting 
(x + -7) equal to 6.32455532 and -6.32455532.


Subproblem 1
x + -7 = 6.32455532

Simplifying
x + -7 = 6.32455532

Reorder the terms:
-7 + x = 6.32455532

Solving
-7 + x = 6.32455532

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 = 6.32455532 + 7

Combine like terms: -7 + 7 = 0
0 + x = 6.32455532 + 7
x = 6.32455532 + 7

Combine like terms: 6.32455532 + 7 = 13.32455532
x = 13.32455532

Simplifying
x = 13.32455532


Subproblem 2
x + -7 = -6.32455532

Simplifying
x + -7 = -6.32455532

Reorder the terms:
-7 + x = -6.32455532

Solving
-7 + x = -6.32455532

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 = -6.32455532 + 7

Combine like terms: -7 + 7 = 0
0 + x = -6.32455532 + 7
x = -6.32455532 + 7

Combine like terms: -6.32455532 + 7 = 0.67544468
x = 0.67544468

Simplifying
x = 0.67544468


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.32455532, 0.67544468}

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