x^2-6x=4.25

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Solution for x^2-6x=4.25 equation: 


Simplifying
x2 + -6x = 4.25

Reorder the terms:
-6x + x2 = 4.25

Solving
-6x + x2 = 4.25

Solving for variable 'x'.

Reorder the terms:
-4.25 + -6x + x2 = 4.25 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
-4.25 + -6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '4.25' to each side of the equation.
-4.25 + -6x + 4.25 + x2 = 0.00 + 4.25

Reorder the terms:
-4.25 + 4.25 + -6x + x2 = 0.00 + 4.25

Combine like terms: -4.25 + 4.25 = 0.00
0.00 + -6x + x2 = 0.00 + 4.25
-6x + x2 = 0.00 + 4.25

Combine like terms: 0.00 + 4.25 = 4.25
-6x + x2 = 4.25

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 4.25 + 9

Reorder the terms:
9 + -6x + x2 = 4.25 + 9

Combine like terms: 4.25 + 9 = 13.25
9 + -6x + x2 = 13.25

Factor a perfect square on the left side:
(x + -3)(x + -3) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(x + -3) equal to 3.640054945 and -3.640054945.


Subproblem 1
x + -3 = 3.640054945

Simplifying
x + -3 = 3.640054945

Reorder the terms:
-3 + x = 3.640054945

Solving
-3 + x = 3.640054945

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.640054945 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.640054945 + 3
x = 3.640054945 + 3

Combine like terms: 3.640054945 + 3 = 6.640054945
x = 6.640054945

Simplifying
x = 6.640054945


Subproblem 2
x + -3 = -3.640054945

Simplifying
x + -3 = -3.640054945

Reorder the terms:
-3 + x = -3.640054945

Solving
-3 + x = -3.640054945

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.640054945 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.640054945 + 3
x = -3.640054945 + 3

Combine like terms: -3.640054945 + 3 = -0.640054945
x = -0.640054945

Simplifying
x = -0.640054945


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.640054945, -0.640054945}

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