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Simplifying h2 + 5h + -26 = 0 Reorder the terms: -26 + 5h + h2 = 0 Solving -26 + 5h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 5h + 26 + h2 = 0 + 26 Reorder the terms: -26 + 26 + 5h + h2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 5h + h2 = 0 + 26 5h + h2 = 0 + 26 Combine like terms: 0 + 26 = 26 5h + h2 = 26 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 = 26 + 6.25 Reorder the terms: 6.25 + 5h + h2 = 26 + 6.25 Combine like terms: 26 + 6.25 = 32.25 6.25 + 5h + h2 = 32.25 Factor a perfect square on the left side: (h + 2.5)(h + 2.5) = 32.25 Calculate the square root of the right side: 5.678908346 Break this problem into two subproblems by setting (h + 2.5) equal to 5.678908346 and -5.678908346.Subproblem 1
h + 2.5 = 5.678908346 Simplifying h + 2.5 = 5.678908346 Reorder the terms: 2.5 + h = 5.678908346 Solving 2.5 + h = 5.678908346 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 = 5.678908346 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = 5.678908346 + -2.5 h = 5.678908346 + -2.5 Combine like terms: 5.678908346 + -2.5 = 3.178908346 h = 3.178908346 Simplifying h = 3.178908346Subproblem 2
h + 2.5 = -5.678908346 Simplifying h + 2.5 = -5.678908346 Reorder the terms: 2.5 + h = -5.678908346 Solving 2.5 + h = -5.678908346 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 = -5.678908346 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = -5.678908346 + -2.5 h = -5.678908346 + -2.5 Combine like terms: -5.678908346 + -2.5 = -8.178908346 h = -8.178908346 Simplifying h = -8.178908346Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.178908346, -8.178908346}
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