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Simplifying h(h + 3) = 20 Reorder the terms: h(3 + h) = 20 (3 * h + h * h) = 20 (3h + h2) = 20 Solving 3h + h2 = 20 Solving for variable 'h'. Reorder the terms: -20 + 3h + h2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 3h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 3h + 20 + h2 = 0 + 20 Reorder the terms: -20 + 20 + 3h + h2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 3h + h2 = 0 + 20 3h + h2 = 0 + 20 Combine like terms: 0 + 20 = 20 3h + h2 = 20 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 = 20 + 2.25 Reorder the terms: 2.25 + 3h + h2 = 20 + 2.25 Combine like terms: 20 + 2.25 = 22.25 2.25 + 3h + h2 = 22.25 Factor a perfect square on the left side: (h + 1.5)(h + 1.5) = 22.25 Calculate the square root of the right side: 4.716990566 Break this problem into two subproblems by setting (h + 1.5) equal to 4.716990566 and -4.716990566.Subproblem 1
h + 1.5 = 4.716990566 Simplifying h + 1.5 = 4.716990566 Reorder the terms: 1.5 + h = 4.716990566 Solving 1.5 + h = 4.716990566 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 = 4.716990566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = 4.716990566 + -1.5 h = 4.716990566 + -1.5 Combine like terms: 4.716990566 + -1.5 = 3.216990566 h = 3.216990566 Simplifying h = 3.216990566Subproblem 2
h + 1.5 = -4.716990566 Simplifying h + 1.5 = -4.716990566 Reorder the terms: 1.5 + h = -4.716990566 Solving 1.5 + h = -4.716990566 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 = -4.716990566 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = -4.716990566 + -1.5 h = -4.716990566 + -1.5 Combine like terms: -4.716990566 + -1.5 = -6.216990566 h = -6.216990566 Simplifying h = -6.216990566Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.216990566, -6.216990566}
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