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Simplifying H2 + 7H = 180 Reorder the terms: 7H + H2 = 180 Solving 7H + H2 = 180 Solving for variable 'H'. Reorder the terms: -180 + 7H + H2 = 180 + -180 Combine like terms: 180 + -180 = 0 -180 + 7H + H2 = 0 Begin completing the square. Move the constant term to the right: Add '180' to each side of the equation. -180 + 7H + 180 + H2 = 0 + 180 Reorder the terms: -180 + 180 + 7H + H2 = 0 + 180 Combine like terms: -180 + 180 = 0 0 + 7H + H2 = 0 + 180 7H + H2 = 0 + 180 Combine like terms: 0 + 180 = 180 7H + H2 = 180 The H term is 7H. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7H + 12.25 + H2 = 180 + 12.25 Reorder the terms: 12.25 + 7H + H2 = 180 + 12.25 Combine like terms: 180 + 12.25 = 192.25 12.25 + 7H + H2 = 192.25 Factor a perfect square on the left side: (H + 3.5)(H + 3.5) = 192.25 Calculate the square root of the right side: 13.865424624 Break this problem into two subproblems by setting (H + 3.5) equal to 13.865424624 and -13.865424624.Subproblem 1
H + 3.5 = 13.865424624 Simplifying H + 3.5 = 13.865424624 Reorder the terms: 3.5 + H = 13.865424624 Solving 3.5 + H = 13.865424624 Solving for variable 'H'. Move all terms containing H to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + H = 13.865424624 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + H = 13.865424624 + -3.5 H = 13.865424624 + -3.5 Combine like terms: 13.865424624 + -3.5 = 10.365424624 H = 10.365424624 Simplifying H = 10.365424624Subproblem 2
H + 3.5 = -13.865424624 Simplifying H + 3.5 = -13.865424624 Reorder the terms: 3.5 + H = -13.865424624 Solving 3.5 + H = -13.865424624 Solving for variable 'H'. Move all terms containing H to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + H = -13.865424624 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + H = -13.865424624 + -3.5 H = -13.865424624 + -3.5 Combine like terms: -13.865424624 + -3.5 = -17.365424624 H = -17.365424624 Simplifying H = -17.365424624Solution
The solution to the problem is based on the solutions from the subproblems. H = {10.365424624, -17.365424624}
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