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Simplifying 5h + h(0.8 + h) = 14 5h + (0.8 * h + h * h) = 14 5h + (0.8h + h2) = 14 Combine like terms: 5h + 0.8h = 5.8h 5.8h + h2 = 14 Solving 5.8h + h2 = 14 Solving for variable 'h'. Reorder the terms: -14 + 5.8h + h2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 5.8h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 5.8h + 14 + h2 = 0 + 14 Reorder the terms: -14 + 14 + 5.8h + h2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 5.8h + h2 = 0 + 14 5.8h + h2 = 0 + 14 Combine like terms: 0 + 14 = 14 5.8h + h2 = 14 The h term is 5.8h. Take half its coefficient (2.9). Square it (8.41) and add it to both sides. Add '8.41' to each side of the equation. 5.8h + 8.41 + h2 = 14 + 8.41 Reorder the terms: 8.41 + 5.8h + h2 = 14 + 8.41 Combine like terms: 14 + 8.41 = 22.41 8.41 + 5.8h + h2 = 22.41 Factor a perfect square on the left side: (h + 2.9)(h + 2.9) = 22.41 Calculate the square root of the right side: 4.733920151 Break this problem into two subproblems by setting (h + 2.9) equal to 4.733920151 and -4.733920151.Subproblem 1
h + 2.9 = 4.733920151 Simplifying h + 2.9 = 4.733920151 Reorder the terms: 2.9 + h = 4.733920151 Solving 2.9 + h = 4.733920151 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + h = 4.733920151 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + h = 4.733920151 + -2.9 h = 4.733920151 + -2.9 Combine like terms: 4.733920151 + -2.9 = 1.833920151 h = 1.833920151 Simplifying h = 1.833920151Subproblem 2
h + 2.9 = -4.733920151 Simplifying h + 2.9 = -4.733920151 Reorder the terms: 2.9 + h = -4.733920151 Solving 2.9 + h = -4.733920151 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-2.9' to each side of the equation. 2.9 + -2.9 + h = -4.733920151 + -2.9 Combine like terms: 2.9 + -2.9 = 0.0 0.0 + h = -4.733920151 + -2.9 h = -4.733920151 + -2.9 Combine like terms: -4.733920151 + -2.9 = -7.633920151 h = -7.633920151 Simplifying h = -7.633920151Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.833920151, -7.633920151}
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