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Simplifying 16h4 + -12h3 + -36h2 = 0 Reorder the terms: -36h2 + -12h3 + 16h4 = 0 Solving -36h2 + -12h3 + 16h4 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '4h2'. 4h2(-9 + -3h + 4h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'h2' equal to zero and attempt to solve: Simplifying h2 = 0 Solving h2 = 0 Move all terms containing h to the left, all other terms to the right. Simplifying h2 = 0 Take the square root of each side: h = {0}Subproblem 2
Set the factor '(-9 + -3h + 4h2)' equal to zero and attempt to solve: Simplifying -9 + -3h + 4h2 = 0 Solving -9 + -3h + 4h2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.25 + -0.75h + h2 = 0 Move the constant term to the right: Add '2.25' to each side of the equation. -2.25 + -0.75h + 2.25 + h2 = 0 + 2.25 Reorder the terms: -2.25 + 2.25 + -0.75h + h2 = 0 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + -0.75h + h2 = 0 + 2.25 -0.75h + h2 = 0 + 2.25 Combine like terms: 0 + 2.25 = 2.25 -0.75h + h2 = 2.25 The h term is -0.75h. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75h + 0.140625 + h2 = 2.25 + 0.140625 Reorder the terms: 0.140625 + -0.75h + h2 = 2.25 + 0.140625 Combine like terms: 2.25 + 0.140625 = 2.390625 0.140625 + -0.75h + h2 = 2.390625 Factor a perfect square on the left side: (h + -0.375)(h + -0.375) = 2.390625 Calculate the square root of the right side: 1.54616461 Break this problem into two subproblems by setting (h + -0.375) equal to 1.54616461 and -1.54616461.Subproblem 1
h + -0.375 = 1.54616461 Simplifying h + -0.375 = 1.54616461 Reorder the terms: -0.375 + h = 1.54616461 Solving -0.375 + h = 1.54616461 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + h = 1.54616461 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + h = 1.54616461 + 0.375 h = 1.54616461 + 0.375 Combine like terms: 1.54616461 + 0.375 = 1.92116461 h = 1.92116461 Simplifying h = 1.92116461Subproblem 2
h + -0.375 = -1.54616461 Simplifying h + -0.375 = -1.54616461 Reorder the terms: -0.375 + h = -1.54616461 Solving -0.375 + h = -1.54616461 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + h = -1.54616461 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + h = -1.54616461 + 0.375 h = -1.54616461 + 0.375 Combine like terms: -1.54616461 + 0.375 = -1.17116461 h = -1.17116461 Simplifying h = -1.17116461Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.92116461, -1.17116461}Solution
h = {0, 1.92116461, -1.17116461}
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