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Simplifying h2 + 5h = 155 Reorder the terms: 5h + h2 = 155 Solving 5h + h2 = 155 Solving for variable 'h'. Reorder the terms: -155 + 5h + h2 = 155 + -155 Combine like terms: 155 + -155 = 0 -155 + 5h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '155' to each side of the equation. -155 + 5h + 155 + h2 = 0 + 155 Reorder the terms: -155 + 155 + 5h + h2 = 0 + 155 Combine like terms: -155 + 155 = 0 0 + 5h + h2 = 0 + 155 5h + h2 = 0 + 155 Combine like terms: 0 + 155 = 155 5h + h2 = 155 The h term is 5h. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5h + 6.25 + h2 = 155 + 6.25 Reorder the terms: 6.25 + 5h + h2 = 155 + 6.25 Combine like terms: 155 + 6.25 = 161.25 6.25 + 5h + h2 = 161.25 Factor a perfect square on the left side: (h + 2.5)(h + 2.5) = 161.25 Calculate the square root of the right side: 12.698425099 Break this problem into two subproblems by setting (h + 2.5) equal to 12.698425099 and -12.698425099.Subproblem 1
h + 2.5 = 12.698425099 Simplifying h + 2.5 = 12.698425099 Reorder the terms: 2.5 + h = 12.698425099 Solving 2.5 + h = 12.698425099 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + h = 12.698425099 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = 12.698425099 + -2.5 h = 12.698425099 + -2.5 Combine like terms: 12.698425099 + -2.5 = 10.198425099 h = 10.198425099 Simplifying h = 10.198425099Subproblem 2
h + 2.5 = -12.698425099 Simplifying h + 2.5 = -12.698425099 Reorder the terms: 2.5 + h = -12.698425099 Solving 2.5 + h = -12.698425099 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + h = -12.698425099 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = -12.698425099 + -2.5 h = -12.698425099 + -2.5 Combine like terms: -12.698425099 + -2.5 = -15.198425099 h = -15.198425099 Simplifying h = -15.198425099Solution
The solution to the problem is based on the solutions from the subproblems. h = {10.198425099, -15.198425099}
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