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Simplifying h2 + 42 = 16h Reorder the terms: 42 + h2 = 16h Solving 42 + h2 = 16h Solving for variable 'h'. Reorder the terms: 42 + -16h + h2 = 16h + -16h Combine like terms: 16h + -16h = 0 42 + -16h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-42' to each side of the equation. 42 + -16h + -42 + h2 = 0 + -42 Reorder the terms: 42 + -42 + -16h + h2 = 0 + -42 Combine like terms: 42 + -42 = 0 0 + -16h + h2 = 0 + -42 -16h + h2 = 0 + -42 Combine like terms: 0 + -42 = -42 -16h + h2 = -42 The h term is -16h. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16h + 64 + h2 = -42 + 64 Reorder the terms: 64 + -16h + h2 = -42 + 64 Combine like terms: -42 + 64 = 22 64 + -16h + h2 = 22 Factor a perfect square on the left side: (h + -8)(h + -8) = 22 Calculate the square root of the right side: 4.69041576 Break this problem into two subproblems by setting (h + -8) equal to 4.69041576 and -4.69041576.Subproblem 1
h + -8 = 4.69041576 Simplifying h + -8 = 4.69041576 Reorder the terms: -8 + h = 4.69041576 Solving -8 + h = 4.69041576 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = 4.69041576 + 8 Combine like terms: -8 + 8 = 0 0 + h = 4.69041576 + 8 h = 4.69041576 + 8 Combine like terms: 4.69041576 + 8 = 12.69041576 h = 12.69041576 Simplifying h = 12.69041576Subproblem 2
h + -8 = -4.69041576 Simplifying h + -8 = -4.69041576 Reorder the terms: -8 + h = -4.69041576 Solving -8 + h = -4.69041576 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + h = -4.69041576 + 8 Combine like terms: -8 + 8 = 0 0 + h = -4.69041576 + 8 h = -4.69041576 + 8 Combine like terms: -4.69041576 + 8 = 3.30958424 h = 3.30958424 Simplifying h = 3.30958424Solution
The solution to the problem is based on the solutions from the subproblems. h = {12.69041576, 3.30958424}
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