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Simplifying 0.02683044 = 3h + -1h2 Solving 0.02683044 = 3h + -1h2 Solving for variable 'h'. Reorder the terms: 0.02683044 + -3h + h2 = 3h + -3h + -1h2 + h2 Combine like terms: 3h + -3h = 0 0.02683044 + -3h + h2 = 0 + -1h2 + h2 0.02683044 + -3h + h2 = -1h2 + h2 Combine like terms: -1h2 + h2 = 0 0.02683044 + -3h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-0.02683044' to each side of the equation. 0.02683044 + -3h + -0.02683044 + h2 = 0 + -0.02683044 Reorder the terms: 0.02683044 + -0.02683044 + -3h + h2 = 0 + -0.02683044 Combine like terms: 0.02683044 + -0.02683044 = 0.00000000 0.00000000 + -3h + h2 = 0 + -0.02683044 -3h + h2 = 0 + -0.02683044 Combine like terms: 0 + -0.02683044 = -0.02683044 -3h + h2 = -0.02683044 The h term is -3h. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3h + 2.25 + h2 = -0.02683044 + 2.25 Reorder the terms: 2.25 + -3h + h2 = -0.02683044 + 2.25 Combine like terms: -0.02683044 + 2.25 = 2.22316956 2.25 + -3h + h2 = 2.22316956 Factor a perfect square on the left side: (h + -1.5)(h + -1.5) = 2.22316956 Calculate the square root of the right side: 1.491029698 Break this problem into two subproblems by setting (h + -1.5) equal to 1.491029698 and -1.491029698.Subproblem 1
h + -1.5 = 1.491029698 Simplifying h + -1.5 = 1.491029698 Reorder the terms: -1.5 + h = 1.491029698 Solving -1.5 + h = 1.491029698 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + h = 1.491029698 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = 1.491029698 + 1.5 h = 1.491029698 + 1.5 Combine like terms: 1.491029698 + 1.5 = 2.991029698 h = 2.991029698 Simplifying h = 2.991029698Subproblem 2
h + -1.5 = -1.491029698 Simplifying h + -1.5 = -1.491029698 Reorder the terms: -1.5 + h = -1.491029698 Solving -1.5 + h = -1.491029698 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + h = -1.491029698 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = -1.491029698 + 1.5 h = -1.491029698 + 1.5 Combine like terms: -1.491029698 + 1.5 = 0.008970302 h = 0.008970302 Simplifying h = 0.008970302Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.991029698, 0.008970302}
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