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Simplifying 0 = -1h2 + 10h + 5 Reorder the terms: 0 = 5 + 10h + -1h2 Solving 0 = 5 + 10h + -1h2 Solving for variable 'h'. Combine like terms: 0 + -5 = -5 -5 + -10h + h2 = 5 + 10h + -1h2 + -5 + -10h + h2 Reorder the terms: -5 + -10h + h2 = 5 + -5 + 10h + -10h + -1h2 + h2 Combine like terms: 5 + -5 = 0 -5 + -10h + h2 = 0 + 10h + -10h + -1h2 + h2 -5 + -10h + h2 = 10h + -10h + -1h2 + h2 Combine like terms: 10h + -10h = 0 -5 + -10h + h2 = 0 + -1h2 + h2 -5 + -10h + h2 = -1h2 + h2 Combine like terms: -1h2 + h2 = 0 -5 + -10h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -10h + 5 + h2 = 0 + 5 Reorder the terms: -5 + 5 + -10h + h2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -10h + h2 = 0 + 5 -10h + h2 = 0 + 5 Combine like terms: 0 + 5 = 5 -10h + h2 = 5 The h term is -10h. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10h + 25 + h2 = 5 + 25 Reorder the terms: 25 + -10h + h2 = 5 + 25 Combine like terms: 5 + 25 = 30 25 + -10h + h2 = 30 Factor a perfect square on the left side: (h + -5)(h + -5) = 30 Calculate the square root of the right side: 5.477225575 Break this problem into two subproblems by setting (h + -5) equal to 5.477225575 and -5.477225575.Subproblem 1
h + -5 = 5.477225575 Simplifying h + -5 = 5.477225575 Reorder the terms: -5 + h = 5.477225575 Solving -5 + h = 5.477225575 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + h = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + h = 5.477225575 + 5 h = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 h = 10.477225575 Simplifying h = 10.477225575Subproblem 2
h + -5 = -5.477225575 Simplifying h + -5 = -5.477225575 Reorder the terms: -5 + h = -5.477225575 Solving -5 + h = -5.477225575 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + h = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + h = -5.477225575 + 5 h = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 h = -0.477225575 Simplifying h = -0.477225575Solution
The solution to the problem is based on the solutions from the subproblems. h = {10.477225575, -0.477225575}
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