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Simplifying h2 + -8h + 31 = 62 Reorder the terms: 31 + -8h + h2 = 62 Solving 31 + -8h + h2 = 62 Solving for variable 'h'. Reorder the terms: 31 + -62 + -8h + h2 = 62 + -62 Combine like terms: 31 + -62 = -31 -31 + -8h + h2 = 62 + -62 Combine like terms: 62 + -62 = 0 -31 + -8h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + -8h + 31 + h2 = 0 + 31 Reorder the terms: -31 + 31 + -8h + h2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -8h + h2 = 0 + 31 -8h + h2 = 0 + 31 Combine like terms: 0 + 31 = 31 -8h + h2 = 31 The h term is -8h. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8h + 16 + h2 = 31 + 16 Reorder the terms: 16 + -8h + h2 = 31 + 16 Combine like terms: 31 + 16 = 47 16 + -8h + h2 = 47 Factor a perfect square on the left side: (h + -4)(h + -4) = 47 Calculate the square root of the right side: 6.8556546 Break this problem into two subproblems by setting (h + -4) equal to 6.8556546 and -6.8556546.Subproblem 1
h + -4 = 6.8556546 Simplifying h + -4 = 6.8556546 Reorder the terms: -4 + h = 6.8556546 Solving -4 + h = 6.8556546 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = 6.8556546 + 4 Combine like terms: -4 + 4 = 0 0 + h = 6.8556546 + 4 h = 6.8556546 + 4 Combine like terms: 6.8556546 + 4 = 10.8556546 h = 10.8556546 Simplifying h = 10.8556546Subproblem 2
h + -4 = -6.8556546 Simplifying h + -4 = -6.8556546 Reorder the terms: -4 + h = -6.8556546 Solving -4 + h = -6.8556546 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = -6.8556546 + 4 Combine like terms: -4 + 4 = 0 0 + h = -6.8556546 + 4 h = -6.8556546 + 4 Combine like terms: -6.8556546 + 4 = -2.8556546 h = -2.8556546 Simplifying h = -2.8556546Solution
The solution to the problem is based on the solutions from the subproblems. h = {10.8556546, -2.8556546}
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