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Simplifying 6h + 58 = 7h(h + 8) + -1h Reorder the terms: 58 + 6h = 7h(h + 8) + -1h Reorder the terms: 58 + 6h = 7h(8 + h) + -1h 58 + 6h = (8 * 7h + h * 7h) + -1h 58 + 6h = (56h + 7h2) + -1h Reorder the terms: 58 + 6h = 56h + -1h + 7h2 Combine like terms: 56h + -1h = 55h 58 + 6h = 55h + 7h2 Solving 58 + 6h = 55h + 7h2 Solving for variable 'h'. Combine like terms: 6h + -55h = -49h 58 + -49h + -7h2 = 55h + 7h2 + -55h + -7h2 Reorder the terms: 58 + -49h + -7h2 = 55h + -55h + 7h2 + -7h2 Combine like terms: 55h + -55h = 0 58 + -49h + -7h2 = 0 + 7h2 + -7h2 58 + -49h + -7h2 = 7h2 + -7h2 Combine like terms: 7h2 + -7h2 = 0 58 + -49h + -7h2 = 0 Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -8.285714286 + 7h + h2 = 0 Move the constant term to the right: Add '8.285714286' to each side of the equation. -8.285714286 + 7h + 8.285714286 + h2 = 0 + 8.285714286 Reorder the terms: -8.285714286 + 8.285714286 + 7h + h2 = 0 + 8.285714286 Combine like terms: -8.285714286 + 8.285714286 = 0.000000000 0.000000000 + 7h + h2 = 0 + 8.285714286 7h + h2 = 0 + 8.285714286 Combine like terms: 0 + 8.285714286 = 8.285714286 7h + h2 = 8.285714286 The h term is 7h. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7h + 12.25 + h2 = 8.285714286 + 12.25 Reorder the terms: 12.25 + 7h + h2 = 8.285714286 + 12.25 Combine like terms: 8.285714286 + 12.25 = 20.535714286 12.25 + 7h + h2 = 20.535714286 Factor a perfect square on the left side: (h + 3.5)(h + 3.5) = 20.535714286 Calculate the square root of the right side: 4.531634836 Break this problem into two subproblems by setting (h + 3.5) equal to 4.531634836 and -4.531634836.Subproblem 1
h + 3.5 = 4.531634836 Simplifying h + 3.5 = 4.531634836 Reorder the terms: 3.5 + h = 4.531634836 Solving 3.5 + h = 4.531634836 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = 4.531634836 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = 4.531634836 + -3.5 h = 4.531634836 + -3.5 Combine like terms: 4.531634836 + -3.5 = 1.031634836 h = 1.031634836 Simplifying h = 1.031634836Subproblem 2
h + 3.5 = -4.531634836 Simplifying h + 3.5 = -4.531634836 Reorder the terms: 3.5 + h = -4.531634836 Solving 3.5 + h = -4.531634836 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + h = -4.531634836 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + h = -4.531634836 + -3.5 h = -4.531634836 + -3.5 Combine like terms: -4.531634836 + -3.5 = -8.031634836 h = -8.031634836 Simplifying h = -8.031634836Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.031634836, -8.031634836}
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