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Simplifying 6x2 + -6x = 32 Reorder the terms: -6x + 6x2 = 32 Solving -6x + 6x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + -6x + 6x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -6x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -3x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -3x + 3x2)' equal to zero and attempt to solve: Simplifying -16 + -3x + 3x2 = 0 Solving -16 + -3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -5.333333333 + -1x + x2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + -1x + 5.333333333 + x2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + -1x + x2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + -1x + x2 = 0 + 5.333333333 -1x + x2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 -1x + x2 = 5.333333333 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 = 5.333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5.333333333 + 0.25 Combine like terms: 5.333333333 + 0.25 = 5.583333333 0.25 + -1x + x2 = 5.583333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 5.583333333 Calculate the square root of the right side: 2.362907813 Break this problem into two subproblems by setting (x + -0.5) equal to 2.362907813 and -2.362907813.Subproblem 1
x + -0.5 = 2.362907813 Simplifying x + -0.5 = 2.362907813 Reorder the terms: -0.5 + x = 2.362907813 Solving -0.5 + x = 2.362907813 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 = 2.362907813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.362907813 + 0.5 x = 2.362907813 + 0.5 Combine like terms: 2.362907813 + 0.5 = 2.862907813 x = 2.862907813 Simplifying x = 2.862907813Subproblem 2
x + -0.5 = -2.362907813 Simplifying x + -0.5 = -2.362907813 Reorder the terms: -0.5 + x = -2.362907813 Solving -0.5 + x = -2.362907813 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 = -2.362907813 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.362907813 + 0.5 x = -2.362907813 + 0.5 Combine like terms: -2.362907813 + 0.5 = -1.862907813 x = -1.862907813 Simplifying x = -1.862907813Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.862907813, -1.862907813}Solution
x = {2.862907813, -1.862907813}
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