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Simplifying h2 + 5h = 295 Reorder the terms: 5h + h2 = 295 Solving 5h + h2 = 295 Solving for variable 'h'. Reorder the terms: -295 + 5h + h2 = 295 + -295 Combine like terms: 295 + -295 = 0 -295 + 5h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '295' to each side of the equation. -295 + 5h + 295 + h2 = 0 + 295 Reorder the terms: -295 + 295 + 5h + h2 = 0 + 295 Combine like terms: -295 + 295 = 0 0 + 5h + h2 = 0 + 295 5h + h2 = 0 + 295 Combine like terms: 0 + 295 = 295 5h + h2 = 295 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 = 295 + 6.25 Reorder the terms: 6.25 + 5h + h2 = 295 + 6.25 Combine like terms: 295 + 6.25 = 301.25 6.25 + 5h + h2 = 301.25 Factor a perfect square on the left side: (h + 2.5)(h + 2.5) = 301.25 Calculate the square root of the right side: 17.356554958 Break this problem into two subproblems by setting (h + 2.5) equal to 17.356554958 and -17.356554958.Subproblem 1
h + 2.5 = 17.356554958 Simplifying h + 2.5 = 17.356554958 Reorder the terms: 2.5 + h = 17.356554958 Solving 2.5 + h = 17.356554958 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 = 17.356554958 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = 17.356554958 + -2.5 h = 17.356554958 + -2.5 Combine like terms: 17.356554958 + -2.5 = 14.856554958 h = 14.856554958 Simplifying h = 14.856554958Subproblem 2
h + 2.5 = -17.356554958 Simplifying h + 2.5 = -17.356554958 Reorder the terms: 2.5 + h = -17.356554958 Solving 2.5 + h = -17.356554958 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 = -17.356554958 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = -17.356554958 + -2.5 h = -17.356554958 + -2.5 Combine like terms: -17.356554958 + -2.5 = -19.856554958 h = -19.856554958 Simplifying h = -19.856554958Solution
The solution to the problem is based on the solutions from the subproblems. h = {14.856554958, -19.856554958}
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