x^2-15x+15=7x

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Solution for x^2-15x+15=7x equation: 


Simplifying
x2 + -15x + 15 = 7x

Reorder the terms:
15 + -15x + x2 = 7x

Solving
15 + -15x + x2 = 7x

Solving for variable 'x'.

Reorder the terms:
15 + -15x + -7x + x2 = 7x + -7x

Combine like terms: -15x + -7x = -22x
15 + -22x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
15 + -22x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + -22x + -15 + x2 = 0 + -15

Reorder the terms:
15 + -15 + -22x + x2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -22x + x2 = 0 + -15
-22x + x2 = 0 + -15

Combine like terms: 0 + -15 = -15
-22x + x2 = -15

The x term is -22x.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22x + 121 + x2 = -15 + 121

Reorder the terms:
121 + -22x + x2 = -15 + 121

Combine like terms: -15 + 121 = 106
121 + -22x + x2 = 106

Factor a perfect square on the left side:
(x + -11)(x + -11) = 106

Calculate the square root of the right side: 10.295630141

Break this problem into two subproblems by setting 
(x + -11) equal to 10.295630141 and -10.295630141.


Subproblem 1
x + -11 = 10.295630141

Simplifying
x + -11 = 10.295630141

Reorder the terms:
-11 + x = 10.295630141

Solving
-11 + x = 10.295630141

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = 10.295630141 + 11

Combine like terms: -11 + 11 = 0
0 + x = 10.295630141 + 11
x = 10.295630141 + 11

Combine like terms: 10.295630141 + 11 = 21.295630141
x = 21.295630141

Simplifying
x = 21.295630141


Subproblem 2
x + -11 = -10.295630141

Simplifying
x + -11 = -10.295630141

Reorder the terms:
-11 + x = -10.295630141

Solving
-11 + x = -10.295630141

Solving for variable 'x'.

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

Add '11' to each side of the equation.
-11 + 11 + x = -10.295630141 + 11

Combine like terms: -11 + 11 = 0
0 + x = -10.295630141 + 11
x = -10.295630141 + 11

Combine like terms: -10.295630141 + 11 = 0.704369859
x = 0.704369859

Simplifying
x = 0.704369859


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.295630141, 0.704369859}

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