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Simplifying h2 + 5h = 270 Reorder the terms: 5h + h2 = 270 Solving 5h + h2 = 270 Solving for variable 'h'. Reorder the terms: -270 + 5h + h2 = 270 + -270 Combine like terms: 270 + -270 = 0 -270 + 5h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '270' to each side of the equation. -270 + 5h + 270 + h2 = 0 + 270 Reorder the terms: -270 + 270 + 5h + h2 = 0 + 270 Combine like terms: -270 + 270 = 0 0 + 5h + h2 = 0 + 270 5h + h2 = 0 + 270 Combine like terms: 0 + 270 = 270 5h + h2 = 270 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 = 270 + 6.25 Reorder the terms: 6.25 + 5h + h2 = 270 + 6.25 Combine like terms: 270 + 6.25 = 276.25 6.25 + 5h + h2 = 276.25 Factor a perfect square on the left side: (h + 2.5)(h + 2.5) = 276.25 Calculate the square root of the right side: 16.620770139 Break this problem into two subproblems by setting (h + 2.5) equal to 16.620770139 and -16.620770139.Subproblem 1
h + 2.5 = 16.620770139 Simplifying h + 2.5 = 16.620770139 Reorder the terms: 2.5 + h = 16.620770139 Solving 2.5 + h = 16.620770139 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 = 16.620770139 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = 16.620770139 + -2.5 h = 16.620770139 + -2.5 Combine like terms: 16.620770139 + -2.5 = 14.120770139 h = 14.120770139 Simplifying h = 14.120770139Subproblem 2
h + 2.5 = -16.620770139 Simplifying h + 2.5 = -16.620770139 Reorder the terms: 2.5 + h = -16.620770139 Solving 2.5 + h = -16.620770139 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 = -16.620770139 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + h = -16.620770139 + -2.5 h = -16.620770139 + -2.5 Combine like terms: -16.620770139 + -2.5 = -19.120770139 h = -19.120770139 Simplifying h = -19.120770139Solution
The solution to the problem is based on the solutions from the subproblems. h = {14.120770139, -19.120770139}
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