6x^2=12x+8

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Solution for 6x^2=12x+8 equation:


Simplifying
6x2 = 12x + 8

Reorder the terms:
6x2 = 8 + 12x

Solving
6x2 = 8 + 12x

Solving for variable 'x'.

Reorder the terms:
-8 + -12x + 6x2 = 8 + 12x + -8 + -12x

Reorder the terms:
-8 + -12x + 6x2 = 8 + -8 + 12x + -12x

Combine like terms: 8 + -8 = 0
-8 + -12x + 6x2 = 0 + 12x + -12x
-8 + -12x + 6x2 = 12x + -12x

Combine like terms: 12x + -12x = 0
-8 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -6x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-4 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying -4 + -6x + 3x2 = 0 Solving -4 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -2x + 1.333333333 + x2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -2x + x2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + 1.333333333 -2x + x2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -2x + x2 = 1.333333333 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 1.333333333 + 1 Reorder the terms: 1 + -2x + x2 = 1.333333333 + 1 Combine like terms: 1.333333333 + 1 = 2.333333333 1 + -2x + x2 = 2.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 2.333333333 Calculate the square root of the right side: 1.527525232 Break this problem into two subproblems by setting (x + -1) equal to 1.527525232 and -1.527525232.

Subproblem 1

x + -1 = 1.527525232 Simplifying x + -1 = 1.527525232 Reorder the terms: -1 + x = 1.527525232 Solving -1 + x = 1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.527525232 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.527525232 + 1 x = 1.527525232 + 1 Combine like terms: 1.527525232 + 1 = 2.527525232 x = 2.527525232 Simplifying x = 2.527525232

Subproblem 2

x + -1 = -1.527525232 Simplifying x + -1 = -1.527525232 Reorder the terms: -1 + x = -1.527525232 Solving -1 + x = -1.527525232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.527525232 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.527525232 + 1 x = -1.527525232 + 1 Combine like terms: -1.527525232 + 1 = -0.527525232 x = -0.527525232 Simplifying x = -0.527525232

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.527525232, -0.527525232}

Solution

x = {2.527525232, -0.527525232}

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