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Simplifying h = -16h2 + 15h + 12 Reorder the terms: h = 12 + 15h + -16h2 Solving h = 12 + 15h + -16h2 Solving for variable 'h'. Reorder the terms: -12 + h + -15h + 16h2 = 12 + 15h + -16h2 + -12 + -15h + 16h2 Combine like terms: h + -15h = -14h -12 + -14h + 16h2 = 12 + 15h + -16h2 + -12 + -15h + 16h2 Reorder the terms: -12 + -14h + 16h2 = 12 + -12 + 15h + -15h + -16h2 + 16h2 Combine like terms: 12 + -12 = 0 -12 + -14h + 16h2 = 0 + 15h + -15h + -16h2 + 16h2 -12 + -14h + 16h2 = 15h + -15h + -16h2 + 16h2 Combine like terms: 15h + -15h = 0 -12 + -14h + 16h2 = 0 + -16h2 + 16h2 -12 + -14h + 16h2 = -16h2 + 16h2 Combine like terms: -16h2 + 16h2 = 0 -12 + -14h + 16h2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + -7h + 8h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -7h + 8h2)' equal to zero and attempt to solve: Simplifying -6 + -7h + 8h2 = 0 Solving -6 + -7h + 8h2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.75 + -0.875h + h2 = 0 Move the constant term to the right: Add '0.75' to each side of the equation. -0.75 + -0.875h + 0.75 + h2 = 0 + 0.75 Reorder the terms: -0.75 + 0.75 + -0.875h + h2 = 0 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + -0.875h + h2 = 0 + 0.75 -0.875h + h2 = 0 + 0.75 Combine like terms: 0 + 0.75 = 0.75 -0.875h + h2 = 0.75 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 = 0.75 + 0.19140625 Reorder the terms: 0.19140625 + -0.875h + h2 = 0.75 + 0.19140625 Combine like terms: 0.75 + 0.19140625 = 0.94140625 0.19140625 + -0.875h + h2 = 0.94140625 Factor a perfect square on the left side: (h + -0.4375)(h + -0.4375) = 0.94140625 Calculate the square root of the right side: 0.970260919 Break this problem into two subproblems by setting (h + -0.4375) equal to 0.970260919 and -0.970260919.Subproblem 1
h + -0.4375 = 0.970260919 Simplifying h + -0.4375 = 0.970260919 Reorder the terms: -0.4375 + h = 0.970260919 Solving -0.4375 + h = 0.970260919 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 = 0.970260919 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + h = 0.970260919 + 0.4375 h = 0.970260919 + 0.4375 Combine like terms: 0.970260919 + 0.4375 = 1.407760919 h = 1.407760919 Simplifying h = 1.407760919Subproblem 2
h + -0.4375 = -0.970260919 Simplifying h + -0.4375 = -0.970260919 Reorder the terms: -0.4375 + h = -0.970260919 Solving -0.4375 + h = -0.970260919 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 = -0.970260919 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + h = -0.970260919 + 0.4375 h = -0.970260919 + 0.4375 Combine like terms: -0.970260919 + 0.4375 = -0.532760919 h = -0.532760919 Simplifying h = -0.532760919Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.407760919, -0.532760919}Solution
h = {1.407760919, -0.532760919}
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