2x^2-4x=x^2+4x-3

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Solution for 2x^2-4x=x^2+4x-3 equation:


Simplifying
2x2 + -4x = x2 + 4x + -3

Reorder the terms:
-4x + 2x2 = x2 + 4x + -3

Reorder the terms:
-4x + 2x2 = -3 + 4x + x2

Solving
-4x + 2x2 = -3 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
3 + -4x + -4x + 2x2 + -1x2 = -3 + 4x + x2 + 3 + -4x + -1x2

Combine like terms: -4x + -4x = -8x
3 + -8x + 2x2 + -1x2 = -3 + 4x + x2 + 3 + -4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
3 + -8x + 1x2 = -3 + 4x + x2 + 3 + -4x + -1x2

Reorder the terms:
3 + -8x + 1x2 = -3 + 3 + 4x + -4x + x2 + -1x2

Combine like terms: -3 + 3 = 0
3 + -8x + 1x2 = 0 + 4x + -4x + x2 + -1x2
3 + -8x + 1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
3 + -8x + 1x2 = 0 + x2 + -1x2
3 + -8x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + -8x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -8x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -8x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -8x + x2 = 0 + -3
-8x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-8x + x2 = -3

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -3 + 16

Reorder the terms:
16 + -8x + x2 = -3 + 16

Combine like terms: -3 + 16 = 13
16 + -8x + x2 = 13

Factor a perfect square on the left side:
(x + -4)(x + -4) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -4) equal to 3.605551275 and -3.605551275.

Subproblem 1

x + -4 = 3.605551275 Simplifying x + -4 = 3.605551275 Reorder the terms: -4 + x = 3.605551275 Solving -4 + x = 3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.605551275 + 4 x = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 x = 7.605551275 Simplifying x = 7.605551275

Subproblem 2

x + -4 = -3.605551275 Simplifying x + -4 = -3.605551275 Reorder the terms: -4 + x = -3.605551275 Solving -4 + x = -3.605551275 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.605551275 + 4 x = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 x = 0.394448725 Simplifying x = 0.394448725

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.605551275, 0.394448725}

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