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Simplifying 14 + h2 = -16h Solving 14 + h2 = -16h Solving for variable 'h'. Reorder the terms: 14 + 16h + h2 = -16h + 16h Combine like terms: -16h + 16h = 0 14 + 16h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + 16h + -14 + h2 = 0 + -14 Reorder the terms: 14 + -14 + 16h + h2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + 16h + h2 = 0 + -14 16h + h2 = 0 + -14 Combine like terms: 0 + -14 = -14 16h + h2 = -14 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 = -14 + 64 Reorder the terms: 64 + 16h + h2 = -14 + 64 Combine like terms: -14 + 64 = 50 64 + 16h + h2 = 50 Factor a perfect square on the left side: (h + 8)(h + 8) = 50 Calculate the square root of the right side: 7.071067812 Break this problem into two subproblems by setting (h + 8) equal to 7.071067812 and -7.071067812.Subproblem 1
h + 8 = 7.071067812 Simplifying h + 8 = 7.071067812 Reorder the terms: 8 + h = 7.071067812 Solving 8 + h = 7.071067812 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 = 7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + h = 7.071067812 + -8 h = 7.071067812 + -8 Combine like terms: 7.071067812 + -8 = -0.928932188 h = -0.928932188 Simplifying h = -0.928932188Subproblem 2
h + 8 = -7.071067812 Simplifying h + 8 = -7.071067812 Reorder the terms: 8 + h = -7.071067812 Solving 8 + h = -7.071067812 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 = -7.071067812 + -8 Combine like terms: 8 + -8 = 0 0 + h = -7.071067812 + -8 h = -7.071067812 + -8 Combine like terms: -7.071067812 + -8 = -15.071067812 h = -15.071067812 Simplifying h = -15.071067812Solution
The solution to the problem is based on the solutions from the subproblems. h = {-0.928932188, -15.071067812}
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