(-x^2)+8x-9=0

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Solution for (-x^2)+8x-9=0 equation: 


Simplifying
(-1x2) + 8x + -9 = 0

Reorder the terms:
-9 + 8x + (-1x2) = 0

Solving
-9 + 8x + (-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 + -8x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -8x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -8x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -8x + x2 = 0 + -9
-8x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-8x + x2 = -9

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -9 + 16

Reorder the terms:
16 + -8x + x2 = -9 + 16

Combine like terms: -9 + 16 = 7
16 + -8x + x2 = 7

Factor a perfect square on the left side:
((x) + -4)((x) + -4) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
((x) + -4) equal to 2.645751311 and -2.645751311.


Subproblem 1
(x) + -4 = 2.645751311

Simplifying
(x) + -4 = 2.645751311
x + -4 = 2.645751311

Reorder the terms:
-4 + x = 2.645751311

Solving
-4 + x = 2.645751311

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 2.645751311 + 4

Combine like terms: -4 + 4 = 0
0 + x = 2.645751311 + 4
x = 2.645751311 + 4

Combine like terms: 2.645751311 + 4 = 6.645751311
x = 6.645751311

Simplifying
x = 6.645751311


Subproblem 2
(x) + -4 = -2.645751311

Simplifying
(x) + -4 = -2.645751311
x + -4 = -2.645751311

Reorder the terms:
-4 + x = -2.645751311

Solving
-4 + x = -2.645751311

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -2.645751311 + 4

Combine like terms: -4 + 4 = 0
0 + x = -2.645751311 + 4
x = -2.645751311 + 4

Combine like terms: -2.645751311 + 4 = 1.354248689
x = 1.354248689

Simplifying
x = 1.354248689


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.645751311, 1.354248689}

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