-x^2+10x-7=0

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Solution for -x^2+10x-7=0 equation: 


Simplifying
-1x2 + 10x + -7 = 0

Reorder the terms:
-7 + 10x + -1x2 = 0

Solving
-7 + 10x + -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'.
7 + -10x + x2 = 0

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + -10x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + -10x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -10x + x2 = 0 + -7
-10x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-10x + x2 = -7

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = -7 + 25

Reorder the terms:
25 + -10x + x2 = -7 + 25

Combine like terms: -7 + 25 = 18
25 + -10x + x2 = 18

Factor a perfect square on the left side:
(x + -5)(x + -5) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + -5) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + -5 = 4.242640687

Simplifying
x + -5 = 4.242640687

Reorder the terms:
-5 + x = 4.242640687

Solving
-5 + x = 4.242640687

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 4.242640687 + 5

Combine like terms: -5 + 5 = 0
0 + x = 4.242640687 + 5
x = 4.242640687 + 5

Combine like terms: 4.242640687 + 5 = 9.242640687
x = 9.242640687

Simplifying
x = 9.242640687


Subproblem 2
x + -5 = -4.242640687

Simplifying
x + -5 = -4.242640687

Reorder the terms:
-5 + x = -4.242640687

Solving
-5 + x = -4.242640687

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -4.242640687 + 5

Combine like terms: -5 + 5 = 0
0 + x = -4.242640687 + 5
x = -4.242640687 + 5

Combine like terms: -4.242640687 + 5 = 0.757359313
x = 0.757359313

Simplifying
x = 0.757359313


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.242640687, 0.757359313}

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