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Simplifying (h + 9)(h + 9) = 5 Reorder the terms: (9 + h)(h + 9) = 5 Reorder the terms: (9 + h)(9 + h) = 5 Multiply (9 + h) * (9 + h) (9(9 + h) + h(9 + h)) = 5 ((9 * 9 + h * 9) + h(9 + h)) = 5 ((81 + 9h) + h(9 + h)) = 5 (81 + 9h + (9 * h + h * h)) = 5 (81 + 9h + (9h + h2)) = 5 Combine like terms: 9h + 9h = 18h (81 + 18h + h2) = 5 Solving 81 + 18h + h2 = 5 Solving for variable 'h'. Reorder the terms: 81 + -5 + 18h + h2 = 5 + -5 Combine like terms: 81 + -5 = 76 76 + 18h + h2 = 5 + -5 Combine like terms: 5 + -5 = 0 76 + 18h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '-76' to each side of the equation. 76 + 18h + -76 + h2 = 0 + -76 Reorder the terms: 76 + -76 + 18h + h2 = 0 + -76 Combine like terms: 76 + -76 = 0 0 + 18h + h2 = 0 + -76 18h + h2 = 0 + -76 Combine like terms: 0 + -76 = -76 18h + h2 = -76 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 = -76 + 81 Reorder the terms: 81 + 18h + h2 = -76 + 81 Combine like terms: -76 + 81 = 5 81 + 18h + h2 = 5 Factor a perfect square on the left side: (h + 9)(h + 9) = 5 Calculate the square root of the right side: 2.236067978 Break this problem into two subproblems by setting (h + 9) equal to 2.236067978 and -2.236067978.Subproblem 1
h + 9 = 2.236067978 Simplifying h + 9 = 2.236067978 Reorder the terms: 9 + h = 2.236067978 Solving 9 + h = 2.236067978 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 = 2.236067978 + -9 Combine like terms: 9 + -9 = 0 0 + h = 2.236067978 + -9 h = 2.236067978 + -9 Combine like terms: 2.236067978 + -9 = -6.763932022 h = -6.763932022 Simplifying h = -6.763932022Subproblem 2
h + 9 = -2.236067978 Simplifying h + 9 = -2.236067978 Reorder the terms: 9 + h = -2.236067978 Solving 9 + h = -2.236067978 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 = -2.236067978 + -9 Combine like terms: 9 + -9 = 0 0 + h = -2.236067978 + -9 h = -2.236067978 + -9 Combine like terms: -2.236067978 + -9 = -11.236067978 h = -11.236067978 Simplifying h = -11.236067978Solution
The solution to the problem is based on the solutions from the subproblems. h = {-6.763932022, -11.236067978}
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