-6+9x=x^2

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Solution for -6+9x=x^2 equation: 


Simplifying
-6 + 9x = x2

Solving
-6 + 9x = x2

Solving for variable 'x'.

Combine like terms: x2 + -1x2 = 0
-6 + 9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
6 + -9x + x2 = 0

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -9x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -9x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -9x + x2 = 0 + -6
-9x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-9x + x2 = -6

The x term is -9x.  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.
-9x + 20.25 + x2 = -6 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -6 + 20.25

Combine like terms: -6 + 20.25 = 14.25
20.25 + -9x + x2 = 14.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.774917218 and -3.774917218.


Subproblem 1
x + -4.5 = 3.774917218

Simplifying
x + -4.5 = 3.774917218

Reorder the terms:
-4.5 + x = 3.774917218

Solving
-4.5 + x = 3.774917218

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 = 3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.774917218 + 4.5
x = 3.774917218 + 4.5

Combine like terms: 3.774917218 + 4.5 = 8.274917218
x = 8.274917218

Simplifying
x = 8.274917218


Subproblem 2
x + -4.5 = -3.774917218

Simplifying
x + -4.5 = -3.774917218

Reorder the terms:
-4.5 + x = -3.774917218

Solving
-4.5 + x = -3.774917218

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 = -3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.774917218 + 4.5
x = -3.774917218 + 4.5

Combine like terms: -3.774917218 + 4.5 = 0.725082782
x = 0.725082782

Simplifying
x = 0.725082782


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.274917218, 0.725082782}

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