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Simplifying h2 + -3h + -405 = 0 Reorder the terms: -405 + -3h + h2 = 0 Solving -405 + -3h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '405' to each side of the equation. -405 + -3h + 405 + h2 = 0 + 405 Reorder the terms: -405 + 405 + -3h + h2 = 0 + 405 Combine like terms: -405 + 405 = 0 0 + -3h + h2 = 0 + 405 -3h + h2 = 0 + 405 Combine like terms: 0 + 405 = 405 -3h + h2 = 405 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 = 405 + 2.25 Reorder the terms: 2.25 + -3h + h2 = 405 + 2.25 Combine like terms: 405 + 2.25 = 407.25 2.25 + -3h + h2 = 407.25 Factor a perfect square on the left side: (h + -1.5)(h + -1.5) = 407.25 Calculate the square root of the right side: 20.180436071 Break this problem into two subproblems by setting (h + -1.5) equal to 20.180436071 and -20.180436071.Subproblem 1
h + -1.5 = 20.180436071 Simplifying h + -1.5 = 20.180436071 Reorder the terms: -1.5 + h = 20.180436071 Solving -1.5 + h = 20.180436071 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 = 20.180436071 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = 20.180436071 + 1.5 h = 20.180436071 + 1.5 Combine like terms: 20.180436071 + 1.5 = 21.680436071 h = 21.680436071 Simplifying h = 21.680436071Subproblem 2
h + -1.5 = -20.180436071 Simplifying h + -1.5 = -20.180436071 Reorder the terms: -1.5 + h = -20.180436071 Solving -1.5 + h = -20.180436071 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 = -20.180436071 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = -20.180436071 + 1.5 h = -20.180436071 + 1.5 Combine like terms: -20.180436071 + 1.5 = -18.680436071 h = -18.680436071 Simplifying h = -18.680436071Solution
The solution to the problem is based on the solutions from the subproblems. h = {21.680436071, -18.680436071}
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