-15x+x^2=10

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Solution for -15x+x^2=10 equation: 


Simplifying
-15x + x2 = 10

Solving
-15x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -15x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -15x + 10 + x2 = 0 + 10

Reorder the terms:
-10 + 10 + -15x + x2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -15x + x2 = 0 + 10
-15x + x2 = 0 + 10

Combine like terms: 0 + 10 = 10
-15x + x2 = 10

The x term is -15x.  Take half its coefficient (-7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
-15x + 56.25 + x2 = 10 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 10 + 56.25

Combine like terms: 10 + 56.25 = 66.25
56.25 + -15x + x2 = 66.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 66.25

Calculate the square root of the right side: 8.139410298

Break this problem into two subproblems by setting 
(x + -7.5) equal to 8.139410298 and -8.139410298.


Subproblem 1
x + -7.5 = 8.139410298

Simplifying
x + -7.5 = 8.139410298

Reorder the terms:
-7.5 + x = 8.139410298

Solving
-7.5 + x = 8.139410298

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = 8.139410298 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 8.139410298 + 7.5
x = 8.139410298 + 7.5

Combine like terms: 8.139410298 + 7.5 = 15.639410298
x = 15.639410298

Simplifying
x = 15.639410298


Subproblem 2
x + -7.5 = -8.139410298

Simplifying
x + -7.5 = -8.139410298

Reorder the terms:
-7.5 + x = -8.139410298

Solving
-7.5 + x = -8.139410298

Solving for variable 'x'.

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

Add '7.5' to each side of the equation.
-7.5 + 7.5 + x = -8.139410298 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -8.139410298 + 7.5
x = -8.139410298 + 7.5

Combine like terms: -8.139410298 + 7.5 = -0.639410298
x = -0.639410298

Simplifying
x = -0.639410298


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.639410298, -0.639410298}

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