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Simplifying 2h2 + -52h = -10 Reorder the terms: -52h + 2h2 = -10 Solving -52h + 2h2 = -10 Solving for variable 'h'. Reorder the terms: 10 + -52h + 2h2 = -10 + 10 Combine like terms: -10 + 10 = 0 10 + -52h + 2h2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -26h + h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -26h + h2)' equal to zero and attempt to solve: Simplifying 5 + -26h + h2 = 0 Solving 5 + -26h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -26h + -5 + h2 = 0 + -5 Reorder the terms: 5 + -5 + -26h + h2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -26h + h2 = 0 + -5 -26h + h2 = 0 + -5 Combine like terms: 0 + -5 = -5 -26h + h2 = -5 The h term is -26h. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26h + 169 + h2 = -5 + 169 Reorder the terms: 169 + -26h + h2 = -5 + 169 Combine like terms: -5 + 169 = 164 169 + -26h + h2 = 164 Factor a perfect square on the left side: (h + -13)(h + -13) = 164 Calculate the square root of the right side: 12.806248475 Break this problem into two subproblems by setting (h + -13) equal to 12.806248475 and -12.806248475.Subproblem 1
h + -13 = 12.806248475 Simplifying h + -13 = 12.806248475 Reorder the terms: -13 + h = 12.806248475 Solving -13 + h = 12.806248475 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + h = 12.806248475 + 13 Combine like terms: -13 + 13 = 0 0 + h = 12.806248475 + 13 h = 12.806248475 + 13 Combine like terms: 12.806248475 + 13 = 25.806248475 h = 25.806248475 Simplifying h = 25.806248475Subproblem 2
h + -13 = -12.806248475 Simplifying h + -13 = -12.806248475 Reorder the terms: -13 + h = -12.806248475 Solving -13 + h = -12.806248475 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + h = -12.806248475 + 13 Combine like terms: -13 + 13 = 0 0 + h = -12.806248475 + 13 h = -12.806248475 + 13 Combine like terms: -12.806248475 + 13 = 0.193751525 h = 0.193751525 Simplifying h = 0.193751525Solution
The solution to the problem is based on the solutions from the subproblems. h = {25.806248475, 0.193751525}Solution
h = {25.806248475, 0.193751525}
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