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Simplifying -8h2 + -7h + 9 = 0 Reorder the terms: 9 + -7h + -8h2 = 0 Solving 9 + -7h + -8h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -1.125 + 0.875h + h2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 0.875h + 1.125 + h2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 0.875h + h2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 0.875h + h2 = 0 + 1.125 0.875h + h2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 0.875h + h2 = 1.125 The h term is 0.875h. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875h + 0.19140625 + h2 = 1.125 + 0.19140625 Reorder the terms: 0.19140625 + 0.875h + h2 = 1.125 + 0.19140625 Combine like terms: 1.125 + 0.19140625 = 1.31640625 0.19140625 + 0.875h + h2 = 1.31640625 Factor a perfect square on the left side: (h + 0.4375)(h + 0.4375) = 1.31640625 Calculate the square root of the right side: 1.147347484 Break this problem into two subproblems by setting (h + 0.4375) equal to 1.147347484 and -1.147347484.Subproblem 1
h + 0.4375 = 1.147347484 Simplifying h + 0.4375 = 1.147347484 Reorder the terms: 0.4375 + h = 1.147347484 Solving 0.4375 + h = 1.147347484 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + h = 1.147347484 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + h = 1.147347484 + -0.4375 h = 1.147347484 + -0.4375 Combine like terms: 1.147347484 + -0.4375 = 0.709847484 h = 0.709847484 Simplifying h = 0.709847484Subproblem 2
h + 0.4375 = -1.147347484 Simplifying h + 0.4375 = -1.147347484 Reorder the terms: 0.4375 + h = -1.147347484 Solving 0.4375 + h = -1.147347484 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + h = -1.147347484 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + h = -1.147347484 + -0.4375 h = -1.147347484 + -0.4375 Combine like terms: -1.147347484 + -0.4375 = -1.584847484 h = -1.584847484 Simplifying h = -1.584847484Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.709847484, -1.584847484}
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