x^2-9.0x=15.7

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Solution for x^2-9.0x=15.7 equation: 


Simplifying
x2 + -9.0x = 15.7

Reorder the terms:
-9.0x + x2 = 15.7

Solving
-9.0x + x2 = 15.7

Solving for variable 'x'.

Reorder the terms:
-15.7 + -9.0x + x2 = 15.7 + -15.7

Combine like terms: 15.7 + -15.7 = 0.0
-15.7 + -9.0x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '15.7' to each side of the equation.
-15.7 + -9.0x + 15.7 + x2 = 0.0 + 15.7

Reorder the terms:
-15.7 + 15.7 + -9.0x + x2 = 0.0 + 15.7

Combine like terms: -15.7 + 15.7 = 0.0
0.0 + -9.0x + x2 = 0.0 + 15.7
-9.0x + x2 = 0.0 + 15.7

Combine like terms: 0.0 + 15.7 = 15.7
-9.0x + x2 = 15.7

The x term is -9.0x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9.0x + 20.25 + x2 = 15.7 + 20.25

Reorder the terms:
20.25 + -9.0x + x2 = 15.7 + 20.25

Combine like terms: 15.7 + 20.25 = 35.95
20.25 + -9.0x + x2 = 35.95

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 35.95

Calculate the square root of the right side: 5.995831886

Break this problem into two subproblems by setting 
(x + -4.5) equal to 5.995831886 and -5.995831886.


Subproblem 1
x + -4.5 = 5.995831886

Simplifying
x + -4.5 = 5.995831886

Reorder the terms:
-4.5 + x = 5.995831886

Solving
-4.5 + x = 5.995831886

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 5.995831886 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 5.995831886 + 4.5
x = 5.995831886 + 4.5

Combine like terms: 5.995831886 + 4.5 = 10.495831886
x = 10.495831886

Simplifying
x = 10.495831886


Subproblem 2
x + -4.5 = -5.995831886

Simplifying
x + -4.5 = -5.995831886

Reorder the terms:
-4.5 + x = -5.995831886

Solving
-4.5 + x = -5.995831886

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -5.995831886 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -5.995831886 + 4.5
x = -5.995831886 + 4.5

Combine like terms: -5.995831886 + 4.5 = -1.495831886
x = -1.495831886

Simplifying
x = -1.495831886


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.495831886, -1.495831886}

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