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Simplifying h(3 + -1h) + -2.25 = 0 (3 * h + -1h * h) + -2.25 = 0 (3h + -1h2) + -2.25 = 0 Reorder the terms: -2.25 + 3h + -1h2 = 0 Solving -2.25 + 3h + -1h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.25 + -3h + h2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -3h + -2.25 + h2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -3h + h2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -3h + h2 = 0 + -2.25 -3h + h2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -3h + h2 = -2.25 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 = -2.25 + 2.25 Reorder the terms: 2.25 + -3h + h2 = -2.25 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 2.25 + -3h + h2 = 0.00 Factor a perfect square on the left side: (h + -1.5)(h + -1.5) = 0.00 Calculate the square root of the right side: 0.00 Break this problem into two subproblems by setting (h + -1.5) equal to 0.00 and 0.00.Subproblem 1
h + -1.5 = 0.00 Simplifying h + -1.5 = 0.00 Reorder the terms: -1.5 + h = 0.00 Solving -1.5 + h = 0.00 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 = 0.00 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = 0.00 + 1.5 h = 0.00 + 1.5 Combine like terms: 0.00 + 1.5 = 1.5 h = 1.5 Simplifying h = 1.5Subproblem 2
h + -1.5 = 0.00 Simplifying h + -1.5 = 0.00 Reorder the terms: -1.5 + h = 0.00 Solving -1.5 + h = 0.00 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 = 0.00 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = 0.00 + 1.5 h = 0.00 + 1.5 Combine like terms: 0.00 + 1.5 = 1.5 h = 1.5 Simplifying h = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.5, 1.5}
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