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Simplifying -8h2 + 5h + 9 = 0 Reorder the terms: 9 + 5h + -8h2 = 0 Solving 9 + 5h + -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 + -0.625h + h2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + -0.625h + 1.125 + h2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + -0.625h + h2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + -0.625h + h2 = 0 + 1.125 -0.625h + h2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 -0.625h + h2 = 1.125 The h term is -0.625h. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625h + 0.09765625 + h2 = 1.125 + 0.09765625 Reorder the terms: 0.09765625 + -0.625h + h2 = 1.125 + 0.09765625 Combine like terms: 1.125 + 0.09765625 = 1.22265625 0.09765625 + -0.625h + h2 = 1.22265625 Factor a perfect square on the left side: (h + -0.3125)(h + -0.3125) = 1.22265625 Calculate the square root of the right side: 1.105737876 Break this problem into two subproblems by setting (h + -0.3125) equal to 1.105737876 and -1.105737876.Subproblem 1
h + -0.3125 = 1.105737876 Simplifying h + -0.3125 = 1.105737876 Reorder the terms: -0.3125 + h = 1.105737876 Solving -0.3125 + h = 1.105737876 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + h = 1.105737876 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + h = 1.105737876 + 0.3125 h = 1.105737876 + 0.3125 Combine like terms: 1.105737876 + 0.3125 = 1.418237876 h = 1.418237876 Simplifying h = 1.418237876Subproblem 2
h + -0.3125 = -1.105737876 Simplifying h + -0.3125 = -1.105737876 Reorder the terms: -0.3125 + h = -1.105737876 Solving -0.3125 + h = -1.105737876 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + h = -1.105737876 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + h = -1.105737876 + 0.3125 h = -1.105737876 + 0.3125 Combine like terms: -1.105737876 + 0.3125 = -0.793237876 h = -0.793237876 Simplifying h = -0.793237876Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.418237876, -0.793237876}
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