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Simplifying 0.5h2 + 8h = 47 Reorder the terms: 8h + 0.5h2 = 47 Solving 8h + 0.5h2 = 47 Solving for variable 'h'. Reorder the terms: -47 + 8h + 0.5h2 = 47 + -47 Combine like terms: 47 + -47 = 0 -47 + 8h + 0.5h2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -94 + 16h + h2 = 0 Move the constant term to the right: Add '94' to each side of the equation. -94 + 16h + 94 + h2 = 0 + 94 Reorder the terms: -94 + 94 + 16h + h2 = 0 + 94 Combine like terms: -94 + 94 = 0 0 + 16h + h2 = 0 + 94 16h + h2 = 0 + 94 Combine like terms: 0 + 94 = 94 16h + h2 = 94 The h term is 16h. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16h + 64 + h2 = 94 + 64 Reorder the terms: 64 + 16h + h2 = 94 + 64 Combine like terms: 94 + 64 = 158 64 + 16h + h2 = 158 Factor a perfect square on the left side: (h + 8)(h + 8) = 158 Calculate the square root of the right side: 12.56980509 Break this problem into two subproblems by setting (h + 8) equal to 12.56980509 and -12.56980509.Subproblem 1
h + 8 = 12.56980509 Simplifying h + 8 = 12.56980509 Reorder the terms: 8 + h = 12.56980509 Solving 8 + h = 12.56980509 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + h = 12.56980509 + -8 Combine like terms: 8 + -8 = 0 0 + h = 12.56980509 + -8 h = 12.56980509 + -8 Combine like terms: 12.56980509 + -8 = 4.56980509 h = 4.56980509 Simplifying h = 4.56980509Subproblem 2
h + 8 = -12.56980509 Simplifying h + 8 = -12.56980509 Reorder the terms: 8 + h = -12.56980509 Solving 8 + h = -12.56980509 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + h = -12.56980509 + -8 Combine like terms: 8 + -8 = 0 0 + h = -12.56980509 + -8 h = -12.56980509 + -8 Combine like terms: -12.56980509 + -8 = -20.56980509 h = -20.56980509 Simplifying h = -20.56980509Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.56980509, -20.56980509}
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