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Simplifying h2 + 16h = 11 Reorder the terms: 16h + h2 = 11 Solving 16h + h2 = 11 Solving for variable 'h'. Reorder the terms: -11 + 16h + h2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 16h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 16h + 11 + h2 = 0 + 11 Reorder the terms: -11 + 11 + 16h + h2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 16h + h2 = 0 + 11 16h + h2 = 0 + 11 Combine like terms: 0 + 11 = 11 16h + h2 = 11 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 = 11 + 64 Reorder the terms: 64 + 16h + h2 = 11 + 64 Combine like terms: 11 + 64 = 75 64 + 16h + h2 = 75 Factor a perfect square on the left side: (h + 8)(h + 8) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (h + 8) equal to 8.660254038 and -8.660254038.Subproblem 1
h + 8 = 8.660254038 Simplifying h + 8 = 8.660254038 Reorder the terms: 8 + h = 8.660254038 Solving 8 + h = 8.660254038 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 = 8.660254038 + -8 Combine like terms: 8 + -8 = 0 0 + h = 8.660254038 + -8 h = 8.660254038 + -8 Combine like terms: 8.660254038 + -8 = 0.660254038 h = 0.660254038 Simplifying h = 0.660254038Subproblem 2
h + 8 = -8.660254038 Simplifying h + 8 = -8.660254038 Reorder the terms: 8 + h = -8.660254038 Solving 8 + h = -8.660254038 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 = -8.660254038 + -8 Combine like terms: 8 + -8 = 0 0 + h = -8.660254038 + -8 h = -8.660254038 + -8 Combine like terms: -8.660254038 + -8 = -16.660254038 h = -16.660254038 Simplifying h = -16.660254038Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.660254038, -16.660254038}
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