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Simplifying 1.5h + h2 + -27 = 0 Reorder the terms: -27 + 1.5h + h2 = 0 Solving -27 + 1.5h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '27' to each side of the equation. -27 + 1.5h + 27 + h2 = 0 + 27 Reorder the terms: -27 + 27 + 1.5h + h2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 1.5h + h2 = 0 + 27 1.5h + h2 = 0 + 27 Combine like terms: 0 + 27 = 27 1.5h + h2 = 27 The h term is 1.5h. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5h + 0.5625 + h2 = 27 + 0.5625 Reorder the terms: 0.5625 + 1.5h + h2 = 27 + 0.5625 Combine like terms: 27 + 0.5625 = 27.5625 0.5625 + 1.5h + h2 = 27.5625 Factor a perfect square on the left side: (h + 0.75)(h + 0.75) = 27.5625 Calculate the square root of the right side: 5.25 Break this problem into two subproblems by setting (h + 0.75) equal to 5.25 and -5.25.Subproblem 1
h + 0.75 = 5.25 Simplifying h + 0.75 = 5.25 Reorder the terms: 0.75 + h = 5.25 Solving 0.75 + h = 5.25 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + h = 5.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + h = 5.25 + -0.75 h = 5.25 + -0.75 Combine like terms: 5.25 + -0.75 = 4.5 h = 4.5 Simplifying h = 4.5Subproblem 2
h + 0.75 = -5.25 Simplifying h + 0.75 = -5.25 Reorder the terms: 0.75 + h = -5.25 Solving 0.75 + h = -5.25 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + h = -5.25 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + h = -5.25 + -0.75 h = -5.25 + -0.75 Combine like terms: -5.25 + -0.75 = -6 h = -6 Simplifying h = -6Solution
The solution to the problem is based on the solutions from the subproblems. h = {4.5, -6}
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