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Simplifying h2 + -148 = 16h Reorder the terms: -148 + h2 = 16h Solving -148 + h2 = 16h Solving for variable 'h'. Reorder the terms: -148 + -16h + h2 = 16h + -16h Combine like terms: 16h + -16h = 0 -148 + -16h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '148' to each side of the equation. -148 + -16h + 148 + h2 = 0 + 148 Reorder the terms: -148 + 148 + -16h + h2 = 0 + 148 Combine like terms: -148 + 148 = 0 0 + -16h + h2 = 0 + 148 -16h + h2 = 0 + 148 Combine like terms: 0 + 148 = 148 -16h + h2 = 148 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 = 148 + 64 Reorder the terms: 64 + -16h + h2 = 148 + 64 Combine like terms: 148 + 64 = 212 64 + -16h + h2 = 212 Factor a perfect square on the left side: (h + -8)(h + -8) = 212 Calculate the square root of the right side: 14.560219779 Break this problem into two subproblems by setting (h + -8) equal to 14.560219779 and -14.560219779.Subproblem 1
h + -8 = 14.560219779 Simplifying h + -8 = 14.560219779 Reorder the terms: -8 + h = 14.560219779 Solving -8 + h = 14.560219779 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 = 14.560219779 + 8 Combine like terms: -8 + 8 = 0 0 + h = 14.560219779 + 8 h = 14.560219779 + 8 Combine like terms: 14.560219779 + 8 = 22.560219779 h = 22.560219779 Simplifying h = 22.560219779Subproblem 2
h + -8 = -14.560219779 Simplifying h + -8 = -14.560219779 Reorder the terms: -8 + h = -14.560219779 Solving -8 + h = -14.560219779 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 = -14.560219779 + 8 Combine like terms: -8 + 8 = 0 0 + h = -14.560219779 + 8 h = -14.560219779 + 8 Combine like terms: -14.560219779 + 8 = -6.560219779 h = -6.560219779 Simplifying h = -6.560219779Solution
The solution to the problem is based on the solutions from the subproblems. h = {22.560219779, -6.560219779}
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