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Simplifying 0.5(h + 6)(h) = 10 Reorder the terms: 0.5(6 + h)(h) = 10 Reorder the terms for easier multiplication: 0.5h(6 + h) = 10 (6 * 0.5h + h * 0.5h) = 10 (3h + 0.5h2) = 10 Solving 3h + 0.5h2 = 10 Solving for variable 'h'. Reorder the terms: -10 + 3h + 0.5h2 = 10 + -10 Combine like terms: 10 + -10 = 0 -10 + 3h + 0.5h2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -20 + 6h + h2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 6h + 20 + h2 = 0 + 20 Reorder the terms: -20 + 20 + 6h + h2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 6h + h2 = 0 + 20 6h + h2 = 0 + 20 Combine like terms: 0 + 20 = 20 6h + h2 = 20 The h term is 6h. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6h + 9 + h2 = 20 + 9 Reorder the terms: 9 + 6h + h2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + 6h + h2 = 29 Factor a perfect square on the left side: (h + 3)(h + 3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (h + 3) equal to 5.385164807 and -5.385164807.Subproblem 1
h + 3 = 5.385164807 Simplifying h + 3 = 5.385164807 Reorder the terms: 3 + h = 5.385164807 Solving 3 + h = 5.385164807 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = 5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + h = 5.385164807 + -3 h = 5.385164807 + -3 Combine like terms: 5.385164807 + -3 = 2.385164807 h = 2.385164807 Simplifying h = 2.385164807Subproblem 2
h + 3 = -5.385164807 Simplifying h + 3 = -5.385164807 Reorder the terms: 3 + h = -5.385164807 Solving 3 + h = -5.385164807 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + h = -5.385164807 + -3 Combine like terms: 3 + -3 = 0 0 + h = -5.385164807 + -3 h = -5.385164807 + -3 Combine like terms: -5.385164807 + -3 = -8.385164807 h = -8.385164807 Simplifying h = -8.385164807Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.385164807, -8.385164807}
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