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Simplifying (h + -2)(h + -6) = 3 Reorder the terms: (-2 + h)(h + -6) = 3 Reorder the terms: (-2 + h)(-6 + h) = 3 Multiply (-2 + h) * (-6 + h) (-2(-6 + h) + h(-6 + h)) = 3 ((-6 * -2 + h * -2) + h(-6 + h)) = 3 ((12 + -2h) + h(-6 + h)) = 3 (12 + -2h + (-6 * h + h * h)) = 3 (12 + -2h + (-6h + h2)) = 3 Combine like terms: -2h + -6h = -8h (12 + -8h + h2) = 3 Solving 12 + -8h + h2 = 3 Solving for variable 'h'. Reorder the terms: 12 + -3 + -8h + h2 = 3 + -3 Combine like terms: 12 + -3 = 9 9 + -8h + h2 = 3 + -3 Combine like terms: 3 + -3 = 0 9 + -8h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -8h + -9 + h2 = 0 + -9 Reorder the terms: 9 + -9 + -8h + h2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -8h + h2 = 0 + -9 -8h + h2 = 0 + -9 Combine like terms: 0 + -9 = -9 -8h + h2 = -9 The h term is -8h. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8h + 16 + h2 = -9 + 16 Reorder the terms: 16 + -8h + h2 = -9 + 16 Combine like terms: -9 + 16 = 7 16 + -8h + h2 = 7 Factor a perfect square on the left side: (h + -4)(h + -4) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (h + -4) equal to 2.645751311 and -2.645751311.Subproblem 1
h + -4 = 2.645751311 Simplifying h + -4 = 2.645751311 Reorder the terms: -4 + h = 2.645751311 Solving -4 + h = 2.645751311 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = 2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + h = 2.645751311 + 4 h = 2.645751311 + 4 Combine like terms: 2.645751311 + 4 = 6.645751311 h = 6.645751311 Simplifying h = 6.645751311Subproblem 2
h + -4 = -2.645751311 Simplifying h + -4 = -2.645751311 Reorder the terms: -4 + h = -2.645751311 Solving -4 + h = -2.645751311 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + h = -2.645751311 + 4 Combine like terms: -4 + 4 = 0 0 + h = -2.645751311 + 4 h = -2.645751311 + 4 Combine like terms: -2.645751311 + 4 = 1.354248689 h = 1.354248689 Simplifying h = 1.354248689Solution
The solution to the problem is based on the solutions from the subproblems. h = {6.645751311, 1.354248689}
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