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Simplifying h2 + 27h + -25 = 0 Reorder the terms: -25 + 27h + h2 = 0 Solving -25 + 27h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + 27h + 25 + h2 = 0 + 25 Reorder the terms: -25 + 25 + 27h + h2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 27h + h2 = 0 + 25 27h + h2 = 0 + 25 Combine like terms: 0 + 25 = 25 27h + h2 = 25 The h term is 27h. Take half its coefficient (13.5). Square it (182.25) and add it to both sides. Add '182.25' to each side of the equation. 27h + 182.25 + h2 = 25 + 182.25 Reorder the terms: 182.25 + 27h + h2 = 25 + 182.25 Combine like terms: 25 + 182.25 = 207.25 182.25 + 27h + h2 = 207.25 Factor a perfect square on the left side: (h + 13.5)(h + 13.5) = 207.25 Calculate the square root of the right side: 14.396180049 Break this problem into two subproblems by setting (h + 13.5) equal to 14.396180049 and -14.396180049.Subproblem 1
h + 13.5 = 14.396180049 Simplifying h + 13.5 = 14.396180049 Reorder the terms: 13.5 + h = 14.396180049 Solving 13.5 + h = 14.396180049 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + h = 14.396180049 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + h = 14.396180049 + -13.5 h = 14.396180049 + -13.5 Combine like terms: 14.396180049 + -13.5 = 0.896180049 h = 0.896180049 Simplifying h = 0.896180049Subproblem 2
h + 13.5 = -14.396180049 Simplifying h + 13.5 = -14.396180049 Reorder the terms: 13.5 + h = -14.396180049 Solving 13.5 + h = -14.396180049 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + h = -14.396180049 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + h = -14.396180049 + -13.5 h = -14.396180049 + -13.5 Combine like terms: -14.396180049 + -13.5 = -27.896180049 h = -27.896180049 Simplifying h = -27.896180049Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.896180049, -27.896180049}
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