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Simplifying -16x2 + 140x + 120 = 0 Reorder the terms: 120 + 140x + -16x2 = 0 Solving 120 + 140x + -16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(30 + 35x + -4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + 35x + -4x2)' equal to zero and attempt to solve: Simplifying 30 + 35x + -4x2 = 0 Solving 30 + 35x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.5 + -8.75x + x2 = 0 Move the constant term to the right: Add '7.5' to each side of the equation. -7.5 + -8.75x + 7.5 + x2 = 0 + 7.5 Reorder the terms: -7.5 + 7.5 + -8.75x + x2 = 0 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + -8.75x + x2 = 0 + 7.5 -8.75x + x2 = 0 + 7.5 Combine like terms: 0 + 7.5 = 7.5 -8.75x + x2 = 7.5 The x term is -8.75x. Take half its coefficient (-4.375). Square it (19.140625) and add it to both sides. Add '19.140625' to each side of the equation. -8.75x + 19.140625 + x2 = 7.5 + 19.140625 Reorder the terms: 19.140625 + -8.75x + x2 = 7.5 + 19.140625 Combine like terms: 7.5 + 19.140625 = 26.640625 19.140625 + -8.75x + x2 = 26.640625 Factor a perfect square on the left side: (x + -4.375)(x + -4.375) = 26.640625 Calculate the square root of the right side: 5.161455706 Break this problem into two subproblems by setting (x + -4.375) equal to 5.161455706 and -5.161455706.Subproblem 1
x + -4.375 = 5.161455706 Simplifying x + -4.375 = 5.161455706 Reorder the terms: -4.375 + x = 5.161455706 Solving -4.375 + x = 5.161455706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = 5.161455706 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = 5.161455706 + 4.375 x = 5.161455706 + 4.375 Combine like terms: 5.161455706 + 4.375 = 9.536455706 x = 9.536455706 Simplifying x = 9.536455706Subproblem 2
x + -4.375 = -5.161455706 Simplifying x + -4.375 = -5.161455706 Reorder the terms: -4.375 + x = -5.161455706 Solving -4.375 + x = -5.161455706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.375' to each side of the equation. -4.375 + 4.375 + x = -5.161455706 + 4.375 Combine like terms: -4.375 + 4.375 = 0.000 0.000 + x = -5.161455706 + 4.375 x = -5.161455706 + 4.375 Combine like terms: -5.161455706 + 4.375 = -0.786455706 x = -0.786455706 Simplifying x = -0.786455706Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.536455706, -0.786455706}Solution
x = {9.536455706, -0.786455706}
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