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Simplifying h(h + 6) = 33.25 Reorder the terms: h(6 + h) = 33.25 (6 * h + h * h) = 33.25 (6h + h2) = 33.25 Solving 6h + h2 = 33.25 Solving for variable 'h'. Reorder the terms: -33.25 + 6h + h2 = 33.25 + -33.25 Combine like terms: 33.25 + -33.25 = 0.00 -33.25 + 6h + h2 = 0.00 Begin completing the square. Move the constant term to the right: Add '33.25' to each side of the equation. -33.25 + 6h + 33.25 + h2 = 0.00 + 33.25 Reorder the terms: -33.25 + 33.25 + 6h + h2 = 0.00 + 33.25 Combine like terms: -33.25 + 33.25 = 0.00 0.00 + 6h + h2 = 0.00 + 33.25 6h + h2 = 0.00 + 33.25 Combine like terms: 0.00 + 33.25 = 33.25 6h + h2 = 33.25 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 = 33.25 + 9 Reorder the terms: 9 + 6h + h2 = 33.25 + 9 Combine like terms: 33.25 + 9 = 42.25 9 + 6h + h2 = 42.25 Factor a perfect square on the left side: (h + 3)(h + 3) = 42.25 Calculate the square root of the right side: 6.5 Break this problem into two subproblems by setting (h + 3) equal to 6.5 and -6.5.Subproblem 1
h + 3 = 6.5 Simplifying h + 3 = 6.5 Reorder the terms: 3 + h = 6.5 Solving 3 + h = 6.5 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 = 6.5 + -3 Combine like terms: 3 + -3 = 0 0 + h = 6.5 + -3 h = 6.5 + -3 Combine like terms: 6.5 + -3 = 3.5 h = 3.5 Simplifying h = 3.5Subproblem 2
h + 3 = -6.5 Simplifying h + 3 = -6.5 Reorder the terms: 3 + h = -6.5 Solving 3 + h = -6.5 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 = -6.5 + -3 Combine like terms: 3 + -3 = 0 0 + h = -6.5 + -3 h = -6.5 + -3 Combine like terms: -6.5 + -3 = -9.5 h = -9.5 Simplifying h = -9.5Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.5, -9.5}
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