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Simplifying h2 + -20h + 25 = 0 Reorder the terms: 25 + -20h + h2 = 0 Solving 25 + -20h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -20h + -25 + h2 = 0 + -25 Reorder the terms: 25 + -25 + -20h + h2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -20h + h2 = 0 + -25 -20h + h2 = 0 + -25 Combine like terms: 0 + -25 = -25 -20h + h2 = -25 The h term is -20h. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20h + 100 + h2 = -25 + 100 Reorder the terms: 100 + -20h + h2 = -25 + 100 Combine like terms: -25 + 100 = 75 100 + -20h + h2 = 75 Factor a perfect square on the left side: (h + -10)(h + -10) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (h + -10) equal to 8.660254038 and -8.660254038.Subproblem 1
h + -10 = 8.660254038 Simplifying h + -10 = 8.660254038 Reorder the terms: -10 + h = 8.660254038 Solving -10 + h = 8.660254038 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + h = 8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + h = 8.660254038 + 10 h = 8.660254038 + 10 Combine like terms: 8.660254038 + 10 = 18.660254038 h = 18.660254038 Simplifying h = 18.660254038Subproblem 2
h + -10 = -8.660254038 Simplifying h + -10 = -8.660254038 Reorder the terms: -10 + h = -8.660254038 Solving -10 + h = -8.660254038 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + h = -8.660254038 + 10 Combine like terms: -10 + 10 = 0 0 + h = -8.660254038 + 10 h = -8.660254038 + 10 Combine like terms: -8.660254038 + 10 = 1.339745962 h = 1.339745962 Simplifying h = 1.339745962Solution
The solution to the problem is based on the solutions from the subproblems. h = {18.660254038, 1.339745962}
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