6x^2-2=-8x

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Solution for 6x^2-2=-8x equation:


Simplifying
6x2 + -2 = -8x

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

Solving
-2 + 6x2 = -8x

Solving for variable 'x'.

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

Combine like terms: -8x + 8x = 0
-2 + 8x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying -1 + 4x + 3x2 = 0 Solving -1 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.3333333333 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '0.3333333333' to each side of the equation. -0.3333333333 + 1.333333333x + 0.3333333333 + x2 = 0 + 0.3333333333 Reorder the terms: -0.3333333333 + 0.3333333333 + 1.333333333x + x2 = 0 + 0.3333333333 Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + 0.3333333333 1.333333333x + x2 = 0 + 0.3333333333 Combine like terms: 0 + 0.3333333333 = 0.3333333333 1.333333333x + x2 = 0.3333333333 The x term is 1.333333333x. Take half its coefficient (0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. 1.333333333x + 0.4444444442 + x2 = 0.3333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 0.3333333333 + 0.4444444442 Combine like terms: 0.3333333333 + 0.4444444442 = 0.7777777775 0.4444444442 + 1.333333333x + x2 = 0.7777777775 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.7777777775 Calculate the square root of the right side: 0.881917104 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.881917104 and -0.881917104.

Subproblem 1

x + 0.6666666665 = 0.881917104 Simplifying x + 0.6666666665 = 0.881917104 Reorder the terms: 0.6666666665 + x = 0.881917104 Solving 0.6666666665 + x = 0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 0.881917104 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.881917104 + -0.6666666665 x = 0.881917104 + -0.6666666665 Combine like terms: 0.881917104 + -0.6666666665 = 0.2152504375 x = 0.2152504375 Simplifying x = 0.2152504375

Subproblem 2

x + 0.6666666665 = -0.881917104 Simplifying x + 0.6666666665 = -0.881917104 Reorder the terms: 0.6666666665 + x = -0.881917104 Solving 0.6666666665 + x = -0.881917104 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -0.881917104 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.881917104 + -0.6666666665 x = -0.881917104 + -0.6666666665 Combine like terms: -0.881917104 + -0.6666666665 = -1.5485837705 x = -1.5485837705 Simplifying x = -1.5485837705

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.2152504375, -1.5485837705}

Solution

x = {0.2152504375, -1.5485837705}

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