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Simplifying 16 + -63h + -1h2 = 0 Solving 16 + -63h + -1h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -16 + 63h + h2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + 63h + 16 + h2 = 0 + 16 Reorder the terms: -16 + 16 + 63h + h2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + 63h + h2 = 0 + 16 63h + h2 = 0 + 16 Combine like terms: 0 + 16 = 16 63h + h2 = 16 The h term is 63h. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63h + 992.25 + h2 = 16 + 992.25 Reorder the terms: 992.25 + 63h + h2 = 16 + 992.25 Combine like terms: 16 + 992.25 = 1008.25 992.25 + 63h + h2 = 1008.25 Factor a perfect square on the left side: (h + 31.5)(h + 31.5) = 1008.25 Calculate the square root of the right side: 31.752952619 Break this problem into two subproblems by setting (h + 31.5) equal to 31.752952619 and -31.752952619.Subproblem 1
h + 31.5 = 31.752952619 Simplifying h + 31.5 = 31.752952619 Reorder the terms: 31.5 + h = 31.752952619 Solving 31.5 + h = 31.752952619 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + h = 31.752952619 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + h = 31.752952619 + -31.5 h = 31.752952619 + -31.5 Combine like terms: 31.752952619 + -31.5 = 0.252952619 h = 0.252952619 Simplifying h = 0.252952619Subproblem 2
h + 31.5 = -31.752952619 Simplifying h + 31.5 = -31.752952619 Reorder the terms: 31.5 + h = -31.752952619 Solving 31.5 + h = -31.752952619 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + h = -31.752952619 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + h = -31.752952619 + -31.5 h = -31.752952619 + -31.5 Combine like terms: -31.752952619 + -31.5 = -63.252952619 h = -63.252952619 Simplifying h = -63.252952619Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.252952619, -63.252952619}
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