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Simplifying (4h + -3) * h = 60 Reorder the terms: (-3 + 4h) * h = 60 Reorder the terms for easier multiplication: h(-3 + 4h) = 60 (-3 * h + 4h * h) = 60 (-3h + 4h2) = 60 Solving -3h + 4h2 = 60 Solving for variable 'h'. Reorder the terms: -60 + -3h + 4h2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -3h + 4h2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -15 + -0.75h + h2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -0.75h + 15 + h2 = 0 + 15 Reorder the terms: -15 + 15 + -0.75h + h2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -0.75h + h2 = 0 + 15 -0.75h + h2 = 0 + 15 Combine like terms: 0 + 15 = 15 -0.75h + h2 = 15 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 = 15 + 0.140625 Reorder the terms: 0.140625 + -0.75h + h2 = 15 + 0.140625 Combine like terms: 15 + 0.140625 = 15.140625 0.140625 + -0.75h + h2 = 15.140625 Factor a perfect square on the left side: (h + -0.375)(h + -0.375) = 15.140625 Calculate the square root of the right side: 3.891095604 Break this problem into two subproblems by setting (h + -0.375) equal to 3.891095604 and -3.891095604.Subproblem 1
h + -0.375 = 3.891095604 Simplifying h + -0.375 = 3.891095604 Reorder the terms: -0.375 + h = 3.891095604 Solving -0.375 + h = 3.891095604 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 = 3.891095604 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + h = 3.891095604 + 0.375 h = 3.891095604 + 0.375 Combine like terms: 3.891095604 + 0.375 = 4.266095604 h = 4.266095604 Simplifying h = 4.266095604Subproblem 2
h + -0.375 = -3.891095604 Simplifying h + -0.375 = -3.891095604 Reorder the terms: -0.375 + h = -3.891095604 Solving -0.375 + h = -3.891095604 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 = -3.891095604 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + h = -3.891095604 + 0.375 h = -3.891095604 + 0.375 Combine like terms: -3.891095604 + 0.375 = -3.516095604 h = -3.516095604 Simplifying h = -3.516095604Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.266095604, -3.516095604}
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