2x(x-1)-6=10(1-x)+6

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Solution for 2x(x-1)-6=10(1-x)+6 equation:


Simplifying
2x(x + -1) + -6 = 10(1 + -1x) + 6

Reorder the terms:
2x(-1 + x) + -6 = 10(1 + -1x) + 6
(-1 * 2x + x * 2x) + -6 = 10(1 + -1x) + 6
(-2x + 2x2) + -6 = 10(1 + -1x) + 6

Reorder the terms:
-6 + -2x + 2x2 = 10(1 + -1x) + 6
-6 + -2x + 2x2 = (1 * 10 + -1x * 10) + 6
-6 + -2x + 2x2 = (10 + -10x) + 6

Reorder the terms:
-6 + -2x + 2x2 = 10 + 6 + -10x

Combine like terms: 10 + 6 = 16
-6 + -2x + 2x2 = 16 + -10x

Solving
-6 + -2x + 2x2 = 16 + -10x

Solving for variable 'x'.

Reorder the terms:
-6 + -16 + -2x + 10x + 2x2 = 16 + -10x + -16 + 10x

Combine like terms: -6 + -16 = -22
-22 + -2x + 10x + 2x2 = 16 + -10x + -16 + 10x

Combine like terms: -2x + 10x = 8x
-22 + 8x + 2x2 = 16 + -10x + -16 + 10x

Reorder the terms:
-22 + 8x + 2x2 = 16 + -16 + -10x + 10x

Combine like terms: 16 + -16 = 0
-22 + 8x + 2x2 = 0 + -10x + 10x
-22 + 8x + 2x2 = -10x + 10x

Combine like terms: -10x + 10x = 0
-22 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-11 + 4x + x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-11 + 4x + x2)' equal to zero and attempt to solve: Simplifying -11 + 4x + x2 = 0 Solving -11 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + 4x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4x + x2 = 0 + 11 4x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 4x + x2 = 11 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 11 + 4 Reorder the terms: 4 + 4x + x2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4x + x2 = 15 Factor a perfect square on the left side: (x + 2)(x + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (x + 2) equal to 3.872983346 and -3.872983346.

Subproblem 1

x + 2 = 3.872983346 Simplifying x + 2 = 3.872983346 Reorder the terms: 2 + x = 3.872983346 Solving 2 + x = 3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.872983346 + -2 x = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 x = 1.872983346 Simplifying x = 1.872983346

Subproblem 2

x + 2 = -3.872983346 Simplifying x + 2 = -3.872983346 Reorder the terms: 2 + x = -3.872983346 Solving 2 + x = -3.872983346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.872983346 + -2 x = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 x = -5.872983346 Simplifying x = -5.872983346

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.872983346, -5.872983346}

Solution

x = {1.872983346, -5.872983346}

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