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Simplifying h2 + 6h + -36 = 0 Reorder the terms: -36 + 6h + h2 = 0 Solving -36 + 6h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '36' to each side of the equation. -36 + 6h + 36 + h2 = 0 + 36 Reorder the terms: -36 + 36 + 6h + h2 = 0 + 36 Combine like terms: -36 + 36 = 0 0 + 6h + h2 = 0 + 36 6h + h2 = 0 + 36 Combine like terms: 0 + 36 = 36 6h + h2 = 36 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 = 36 + 9 Reorder the terms: 9 + 6h + h2 = 36 + 9 Combine like terms: 36 + 9 = 45 9 + 6h + h2 = 45 Factor a perfect square on the left side: (h + 3)(h + 3) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (h + 3) equal to 6.708203933 and -6.708203933.Subproblem 1
h + 3 = 6.708203933 Simplifying h + 3 = 6.708203933 Reorder the terms: 3 + h = 6.708203933 Solving 3 + h = 6.708203933 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 = 6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + h = 6.708203933 + -3 h = 6.708203933 + -3 Combine like terms: 6.708203933 + -3 = 3.708203933 h = 3.708203933 Simplifying h = 3.708203933Subproblem 2
h + 3 = -6.708203933 Simplifying h + 3 = -6.708203933 Reorder the terms: 3 + h = -6.708203933 Solving 3 + h = -6.708203933 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 = -6.708203933 + -3 Combine like terms: 3 + -3 = 0 0 + h = -6.708203933 + -3 h = -6.708203933 + -3 Combine like terms: -6.708203933 + -3 = -9.708203933 h = -9.708203933 Simplifying h = -9.708203933Solution
The solution to the problem is based on the solutions from the subproblems. h = {3.708203933, -9.708203933}
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