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Simplifying h2 = 9h + 18 Reorder the terms: h2 = 18 + 9h Solving h2 = 18 + 9h Solving for variable 'h'. Reorder the terms: -18 + -9h + h2 = 18 + 9h + -18 + -9h Reorder the terms: -18 + -9h + h2 = 18 + -18 + 9h + -9h Combine like terms: 18 + -18 = 0 -18 + -9h + h2 = 0 + 9h + -9h -18 + -9h + h2 = 9h + -9h Combine like terms: 9h + -9h = 0 -18 + -9h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -9h + 18 + h2 = 0 + 18 Reorder the terms: -18 + 18 + -9h + h2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -9h + h2 = 0 + 18 -9h + h2 = 0 + 18 Combine like terms: 0 + 18 = 18 -9h + h2 = 18 The h term is -9h. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9h + 20.25 + h2 = 18 + 20.25 Reorder the terms: 20.25 + -9h + h2 = 18 + 20.25 Combine like terms: 18 + 20.25 = 38.25 20.25 + -9h + h2 = 38.25 Factor a perfect square on the left side: (h + -4.5)(h + -4.5) = 38.25 Calculate the square root of the right side: 6.184658438 Break this problem into two subproblems by setting (h + -4.5) equal to 6.184658438 and -6.184658438.Subproblem 1
h + -4.5 = 6.184658438 Simplifying h + -4.5 = 6.184658438 Reorder the terms: -4.5 + h = 6.184658438 Solving -4.5 + h = 6.184658438 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + h = 6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + h = 6.184658438 + 4.5 h = 6.184658438 + 4.5 Combine like terms: 6.184658438 + 4.5 = 10.684658438 h = 10.684658438 Simplifying h = 10.684658438Subproblem 2
h + -4.5 = -6.184658438 Simplifying h + -4.5 = -6.184658438 Reorder the terms: -4.5 + h = -6.184658438 Solving -4.5 + h = -6.184658438 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + h = -6.184658438 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + h = -6.184658438 + 4.5 h = -6.184658438 + 4.5 Combine like terms: -6.184658438 + 4.5 = -1.684658438 h = -1.684658438 Simplifying h = -1.684658438Solution
The solution to the problem is based on the solutions from the subproblems. h = {10.684658438, -1.684658438}
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