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Simplifying (h + 9)(h + 9) = 3 Reorder the terms: (9 + h)(h + 9) = 3 Reorder the terms: (9 + h)(9 + h) = 3 Multiply (9 + h) * (9 + h) (9(9 + h) + h(9 + h)) = 3 ((9 * 9 + h * 9) + h(9 + h)) = 3 ((81 + 9h) + h(9 + h)) = 3 (81 + 9h + (9 * h + h * h)) = 3 (81 + 9h + (9h + h2)) = 3 Combine like terms: 9h + 9h = 18h (81 + 18h + h2) = 3 Solving 81 + 18h + h2 = 3 Solving for variable 'h'. Reorder the terms: 81 + -3 + 18h + h2 = 3 + -3 Combine like terms: 81 + -3 = 78 78 + 18h + h2 = 3 + -3 Combine like terms: 3 + -3 = 0 78 + 18h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-78' to each side of the equation. 78 + 18h + -78 + h2 = 0 + -78 Reorder the terms: 78 + -78 + 18h + h2 = 0 + -78 Combine like terms: 78 + -78 = 0 0 + 18h + h2 = 0 + -78 18h + h2 = 0 + -78 Combine like terms: 0 + -78 = -78 18h + h2 = -78 The h term is 18h. Take half its coefficient (9). Square it (81) and add it to both sides. Add '81' to each side of the equation. 18h + 81 + h2 = -78 + 81 Reorder the terms: 81 + 18h + h2 = -78 + 81 Combine like terms: -78 + 81 = 3 81 + 18h + h2 = 3 Factor a perfect square on the left side: (h + 9)(h + 9) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (h + 9) equal to 1.732050808 and -1.732050808.Subproblem 1
h + 9 = 1.732050808 Simplifying h + 9 = 1.732050808 Reorder the terms: 9 + h = 1.732050808 Solving 9 + h = 1.732050808 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + h = 1.732050808 + -9 Combine like terms: 9 + -9 = 0 0 + h = 1.732050808 + -9 h = 1.732050808 + -9 Combine like terms: 1.732050808 + -9 = -7.267949192 h = -7.267949192 Simplifying h = -7.267949192Subproblem 2
h + 9 = -1.732050808 Simplifying h + 9 = -1.732050808 Reorder the terms: 9 + h = -1.732050808 Solving 9 + h = -1.732050808 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + h = -1.732050808 + -9 Combine like terms: 9 + -9 = 0 0 + h = -1.732050808 + -9 h = -1.732050808 + -9 Combine like terms: -1.732050808 + -9 = -10.732050808 h = -10.732050808 Simplifying h = -10.732050808Solution
The solution to the problem is based on the solutions from the subproblems. h = {-7.267949192, -10.732050808}
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