2x(4x-3)-8=4+2x

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Solution for 2x(4x-3)-8=4+2x equation:


Simplifying
2x(4x + -3) + -8 = 4 + 2x

Reorder the terms:
2x(-3 + 4x) + -8 = 4 + 2x
(-3 * 2x + 4x * 2x) + -8 = 4 + 2x
(-6x + 8x2) + -8 = 4 + 2x

Reorder the terms:
-8 + -6x + 8x2 = 4 + 2x

Solving
-8 + -6x + 8x2 = 4 + 2x

Solving for variable 'x'.

Reorder the terms:
-8 + -4 + -6x + -2x + 8x2 = 4 + 2x + -4 + -2x

Combine like terms: -8 + -4 = -12
-12 + -6x + -2x + 8x2 = 4 + 2x + -4 + -2x

Combine like terms: -6x + -2x = -8x
-12 + -8x + 8x2 = 4 + 2x + -4 + -2x

Reorder the terms:
-12 + -8x + 8x2 = 4 + -4 + 2x + -2x

Combine like terms: 4 + -4 = 0
-12 + -8x + 8x2 = 0 + 2x + -2x
-12 + -8x + 8x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-12 + -8x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -2x + 2x2) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(-3 + -2x + 2x2)' equal to zero and attempt to solve: Simplifying -3 + -2x + 2x2 = 0 Solving -3 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -1.5 + -1x + x2 = 0 Move the constant term to the right: Add '1.5' to each side of the equation. -1.5 + -1x + 1.5 + x2 = 0 + 1.5 Reorder the terms: -1.5 + 1.5 + -1x + x2 = 0 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + -1x + x2 = 0 + 1.5 -1x + x2 = 0 + 1.5 Combine like terms: 0 + 1.5 = 1.5 -1x + x2 = 1.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 1.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.5 + 0.25 Combine like terms: 1.5 + 0.25 = 1.75 0.25 + -1x + x2 = 1.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.75 Calculate the square root of the right side: 1.322875656 Break this problem into two subproblems by setting (x + -0.5) equal to 1.322875656 and -1.322875656.

Subproblem 1

x + -0.5 = 1.322875656 Simplifying x + -0.5 = 1.322875656 Reorder the terms: -0.5 + x = 1.322875656 Solving -0.5 + x = 1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.322875656 + 0.5 x = 1.322875656 + 0.5 Combine like terms: 1.322875656 + 0.5 = 1.822875656 x = 1.822875656 Simplifying x = 1.822875656

Subproblem 2

x + -0.5 = -1.322875656 Simplifying x + -0.5 = -1.322875656 Reorder the terms: -0.5 + x = -1.322875656 Solving -0.5 + x = -1.322875656 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -1.322875656 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.322875656 + 0.5 x = -1.322875656 + 0.5 Combine like terms: -1.322875656 + 0.5 = -0.822875656 x = -0.822875656 Simplifying x = -0.822875656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.822875656, -0.822875656}

Solution

x = {1.822875656, -0.822875656}

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