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Simplifying 17x(4x + -6) = 32 Reorder the terms: 17x(-6 + 4x) = 32 (-6 * 17x + 4x * 17x) = 32 (-102x + 68x2) = 32 Solving -102x + 68x2 = 32 Solving for variable 'x'. Reorder the terms: -32 + -102x + 68x2 = 32 + -32 Combine like terms: 32 + -32 = 0 -32 + -102x + 68x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-16 + -51x + 34x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-16 + -51x + 34x2)' equal to zero and attempt to solve: Simplifying -16 + -51x + 34x2 = 0 Solving -16 + -51x + 34x2 = 0 Begin completing the square. Divide all terms by 34 the coefficient of the squared term: Divide each side by '34'. -0.4705882353 + -1.5x + x2 = 0 Move the constant term to the right: Add '0.4705882353' to each side of the equation. -0.4705882353 + -1.5x + 0.4705882353 + x2 = 0 + 0.4705882353 Reorder the terms: -0.4705882353 + 0.4705882353 + -1.5x + x2 = 0 + 0.4705882353 Combine like terms: -0.4705882353 + 0.4705882353 = 0.0000000000 0.0000000000 + -1.5x + x2 = 0 + 0.4705882353 -1.5x + x2 = 0 + 0.4705882353 Combine like terms: 0 + 0.4705882353 = 0.4705882353 -1.5x + x2 = 0.4705882353 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 0.4705882353 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 0.4705882353 + 0.5625 Combine like terms: 0.4705882353 + 0.5625 = 1.0330882353 0.5625 + -1.5x + x2 = 1.0330882353 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 1.0330882353 Calculate the square root of the right side: 1.016409482 Break this problem into two subproblems by setting (x + -0.75) equal to 1.016409482 and -1.016409482.Subproblem 1
x + -0.75 = 1.016409482 Simplifying x + -0.75 = 1.016409482 Reorder the terms: -0.75 + x = 1.016409482 Solving -0.75 + x = 1.016409482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 1.016409482 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 1.016409482 + 0.75 x = 1.016409482 + 0.75 Combine like terms: 1.016409482 + 0.75 = 1.766409482 x = 1.766409482 Simplifying x = 1.766409482Subproblem 2
x + -0.75 = -1.016409482 Simplifying x + -0.75 = -1.016409482 Reorder the terms: -0.75 + x = -1.016409482 Solving -0.75 + x = -1.016409482 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -1.016409482 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -1.016409482 + 0.75 x = -1.016409482 + 0.75 Combine like terms: -1.016409482 + 0.75 = -0.266409482 x = -0.266409482 Simplifying x = -0.266409482Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.766409482, -0.266409482}Solution
x = {1.766409482, -0.266409482}
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