2x^2-6x=x^2+6x-3

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Solution for 2x^2-6x=x^2+6x-3 equation:


Simplifying
2x2 + -6x = x2 + 6x + -3

Reorder the terms:
-6x + 2x2 = x2 + 6x + -3

Reorder the terms:
-6x + 2x2 = -3 + 6x + x2

Solving
-6x + 2x2 = -3 + 6x + x2

Solving for variable 'x'.

Reorder the terms:
3 + -6x + -6x + 2x2 + -1x2 = -3 + 6x + x2 + 3 + -6x + -1x2

Combine like terms: -6x + -6x = -12x
3 + -12x + 2x2 + -1x2 = -3 + 6x + x2 + 3 + -6x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
3 + -12x + 1x2 = -3 + 6x + x2 + 3 + -6x + -1x2

Reorder the terms:
3 + -12x + 1x2 = -3 + 3 + 6x + -6x + x2 + -1x2

Combine like terms: -3 + 3 = 0
3 + -12x + 1x2 = 0 + 6x + -6x + x2 + -1x2
3 + -12x + 1x2 = 6x + -6x + x2 + -1x2

Combine like terms: 6x + -6x = 0
3 + -12x + 1x2 = 0 + x2 + -1x2
3 + -12x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -12x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -12x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -12x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -12x + x2 = 0 + -3
-12x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-12x + x2 = -3

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -3 + 36

Reorder the terms:
36 + -12x + x2 = -3 + 36

Combine like terms: -3 + 36 = 33
36 + -12x + x2 = 33

Factor a perfect square on the left side:
(x + -6)(x + -6) = 33

Calculate the square root of the right side: 5.744562647

Break this problem into two subproblems by setting 
(x + -6) equal to 5.744562647 and -5.744562647.

Subproblem 1

x + -6 = 5.744562647 Simplifying x + -6 = 5.744562647 Reorder the terms: -6 + x = 5.744562647 Solving -6 + x = 5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = 5.744562647 + 6 x = 5.744562647 + 6 Combine like terms: 5.744562647 + 6 = 11.744562647 x = 11.744562647 Simplifying x = 11.744562647

Subproblem 2

x + -6 = -5.744562647 Simplifying x + -6 = -5.744562647 Reorder the terms: -6 + x = -5.744562647 Solving -6 + x = -5.744562647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -5.744562647 + 6 Combine like terms: -6 + 6 = 0 0 + x = -5.744562647 + 6 x = -5.744562647 + 6 Combine like terms: -5.744562647 + 6 = 0.255437353 x = 0.255437353 Simplifying x = 0.255437353

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.744562647, 0.255437353}

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