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Simplifying (h + 8)(h + 2) = 100 Reorder the terms: (8 + h)(h + 2) = 100 Reorder the terms: (8 + h)(2 + h) = 100 Multiply (8 + h) * (2 + h) (8(2 + h) + h(2 + h)) = 100 ((2 * 8 + h * 8) + h(2 + h)) = 100 ((16 + 8h) + h(2 + h)) = 100 (16 + 8h + (2 * h + h * h)) = 100 (16 + 8h + (2h + h2)) = 100 Combine like terms: 8h + 2h = 10h (16 + 10h + h2) = 100 Solving 16 + 10h + h2 = 100 Solving for variable 'h'. Reorder the terms: 16 + -100 + 10h + h2 = 100 + -100 Combine like terms: 16 + -100 = -84 -84 + 10h + h2 = 100 + -100 Combine like terms: 100 + -100 = 0 -84 + 10h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '84' to each side of the equation. -84 + 10h + 84 + h2 = 0 + 84 Reorder the terms: -84 + 84 + 10h + h2 = 0 + 84 Combine like terms: -84 + 84 = 0 0 + 10h + h2 = 0 + 84 10h + h2 = 0 + 84 Combine like terms: 0 + 84 = 84 10h + h2 = 84 The h term is 10h. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10h + 25 + h2 = 84 + 25 Reorder the terms: 25 + 10h + h2 = 84 + 25 Combine like terms: 84 + 25 = 109 25 + 10h + h2 = 109 Factor a perfect square on the left side: (h + 5)(h + 5) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (h + 5) equal to 10.440306509 and -10.440306509.Subproblem 1
h + 5 = 10.440306509 Simplifying h + 5 = 10.440306509 Reorder the terms: 5 + h = 10.440306509 Solving 5 + h = 10.440306509 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = 10.440306509 + -5 Combine like terms: 5 + -5 = 0 0 + h = 10.440306509 + -5 h = 10.440306509 + -5 Combine like terms: 10.440306509 + -5 = 5.440306509 h = 5.440306509 Simplifying h = 5.440306509Subproblem 2
h + 5 = -10.440306509 Simplifying h + 5 = -10.440306509 Reorder the terms: 5 + h = -10.440306509 Solving 5 + h = -10.440306509 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + h = -10.440306509 + -5 Combine like terms: 5 + -5 = 0 0 + h = -10.440306509 + -5 h = -10.440306509 + -5 Combine like terms: -10.440306509 + -5 = -15.440306509 h = -15.440306509 Simplifying h = -15.440306509Solution
The solution to the problem is based on the solutions from the subproblems. h = {5.440306509, -15.440306509}
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