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Simplifying 2h2 + 52h = -58 Reorder the terms: 52h + 2h2 = -58 Solving 52h + 2h2 = -58 Solving for variable 'h'. Reorder the terms: 58 + 52h + 2h2 = -58 + 58 Combine like terms: -58 + 58 = 0 58 + 52h + 2h2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(29 + 26h + h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + 26h + h2)' equal to zero and attempt to solve: Simplifying 29 + 26h + h2 = 0 Solving 29 + 26h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-29' to each side of the equation. 29 + 26h + -29 + h2 = 0 + -29 Reorder the terms: 29 + -29 + 26h + h2 = 0 + -29 Combine like terms: 29 + -29 = 0 0 + 26h + h2 = 0 + -29 26h + h2 = 0 + -29 Combine like terms: 0 + -29 = -29 26h + h2 = -29 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 = -29 + 169 Reorder the terms: 169 + 26h + h2 = -29 + 169 Combine like terms: -29 + 169 = 140 169 + 26h + h2 = 140 Factor a perfect square on the left side: (h + 13)(h + 13) = 140 Calculate the square root of the right side: 11.832159566 Break this problem into two subproblems by setting (h + 13) equal to 11.832159566 and -11.832159566.Subproblem 1
h + 13 = 11.832159566 Simplifying h + 13 = 11.832159566 Reorder the terms: 13 + h = 11.832159566 Solving 13 + h = 11.832159566 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 = 11.832159566 + -13 Combine like terms: 13 + -13 = 0 0 + h = 11.832159566 + -13 h = 11.832159566 + -13 Combine like terms: 11.832159566 + -13 = -1.167840434 h = -1.167840434 Simplifying h = -1.167840434Subproblem 2
h + 13 = -11.832159566 Simplifying h + 13 = -11.832159566 Reorder the terms: 13 + h = -11.832159566 Solving 13 + h = -11.832159566 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 = -11.832159566 + -13 Combine like terms: 13 + -13 = 0 0 + h = -11.832159566 + -13 h = -11.832159566 + -13 Combine like terms: -11.832159566 + -13 = -24.832159566 h = -24.832159566 Simplifying h = -24.832159566Solution
The solution to the problem is based on the solutions from the subproblems. h = {-1.167840434, -24.832159566}Solution
h = {-1.167840434, -24.832159566}
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