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Simplifying 0 = 8h2 + 24h + -570 Reorder the terms: 0 = -570 + 24h + 8h2 Solving 0 = -570 + 24h + 8h2 Solving for variable 'h'. Combine like terms: 0 + 570 = 570 570 + -24h + -8h2 = -570 + 24h + 8h2 + 570 + -24h + -8h2 Reorder the terms: 570 + -24h + -8h2 = -570 + 570 + 24h + -24h + 8h2 + -8h2 Combine like terms: -570 + 570 = 0 570 + -24h + -8h2 = 0 + 24h + -24h + 8h2 + -8h2 570 + -24h + -8h2 = 24h + -24h + 8h2 + -8h2 Combine like terms: 24h + -24h = 0 570 + -24h + -8h2 = 0 + 8h2 + -8h2 570 + -24h + -8h2 = 8h2 + -8h2 Combine like terms: 8h2 + -8h2 = 0 570 + -24h + -8h2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(285 + -12h + -4h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(285 + -12h + -4h2)' equal to zero and attempt to solve: Simplifying 285 + -12h + -4h2 = 0 Solving 285 + -12h + -4h2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -71.25 + 3h + h2 = 0 Move the constant term to the right: Add '71.25' to each side of the equation. -71.25 + 3h + 71.25 + h2 = 0 + 71.25 Reorder the terms: -71.25 + 71.25 + 3h + h2 = 0 + 71.25 Combine like terms: -71.25 + 71.25 = 0.00 0.00 + 3h + h2 = 0 + 71.25 3h + h2 = 0 + 71.25 Combine like terms: 0 + 71.25 = 71.25 3h + h2 = 71.25 The h term is 3h. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3h + 2.25 + h2 = 71.25 + 2.25 Reorder the terms: 2.25 + 3h + h2 = 71.25 + 2.25 Combine like terms: 71.25 + 2.25 = 73.5 2.25 + 3h + h2 = 73.5 Factor a perfect square on the left side: (h + 1.5)(h + 1.5) = 73.5 Calculate the square root of the right side: 8.5732141 Break this problem into two subproblems by setting (h + 1.5) equal to 8.5732141 and -8.5732141.Subproblem 1
h + 1.5 = 8.5732141 Simplifying h + 1.5 = 8.5732141 Reorder the terms: 1.5 + h = 8.5732141 Solving 1.5 + h = 8.5732141 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = 8.5732141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = 8.5732141 + -1.5 h = 8.5732141 + -1.5 Combine like terms: 8.5732141 + -1.5 = 7.0732141 h = 7.0732141 Simplifying h = 7.0732141Subproblem 2
h + 1.5 = -8.5732141 Simplifying h + 1.5 = -8.5732141 Reorder the terms: 1.5 + h = -8.5732141 Solving 1.5 + h = -8.5732141 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = -8.5732141 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = -8.5732141 + -1.5 h = -8.5732141 + -1.5 Combine like terms: -8.5732141 + -1.5 = -10.0732141 h = -10.0732141 Simplifying h = -10.0732141Solution
The solution to the problem is based on the solutions from the subproblems. h = {7.0732141, -10.0732141}Solution
h = {7.0732141, -10.0732141}
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