6x^2+8x-32=0

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Solution for 6x^2+8x-32=0 equation:


Simplifying
6x2 + 8x + -32 = 0

Reorder the terms:
-32 + 8x + 6x2 = 0

Solving
-32 + 8x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-16 + 4x + 3x2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-16 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying -16 + 4x + 3x2 = 0 Solving -16 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 1.333333333x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 1.333333333x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + 5.333333333 1.333333333x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 1.333333333x + x2 = 5.333333333 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 = 5.333333333 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 5.333333333 + 0.4444444442 Combine like terms: 5.333333333 + 0.4444444442 = 5.7777777772 0.4444444442 + 1.333333333x + x2 = 5.7777777772 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 5.7777777772 Calculate the square root of the right side: 2.40370085 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 2.40370085 and -2.40370085.

Subproblem 1

x + 0.6666666665 = 2.40370085 Simplifying x + 0.6666666665 = 2.40370085 Reorder the terms: 0.6666666665 + x = 2.40370085 Solving 0.6666666665 + x = 2.40370085 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 = 2.40370085 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 2.40370085 + -0.6666666665 x = 2.40370085 + -0.6666666665 Combine like terms: 2.40370085 + -0.6666666665 = 1.7370341835 x = 1.7370341835 Simplifying x = 1.7370341835

Subproblem 2

x + 0.6666666665 = -2.40370085 Simplifying x + 0.6666666665 = -2.40370085 Reorder the terms: 0.6666666665 + x = -2.40370085 Solving 0.6666666665 + x = -2.40370085 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 = -2.40370085 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -2.40370085 + -0.6666666665 x = -2.40370085 + -0.6666666665 Combine like terms: -2.40370085 + -0.6666666665 = -3.0703675165 x = -3.0703675165 Simplifying x = -3.0703675165

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7370341835, -3.0703675165}

Solution

x = {1.7370341835, -3.0703675165}

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