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Simplifying h2 + 23h + -44 = 0 Reorder the terms: -44 + 23h + h2 = 0 Solving -44 + 23h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '44' to each side of the equation. -44 + 23h + 44 + h2 = 0 + 44 Reorder the terms: -44 + 44 + 23h + h2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + 23h + h2 = 0 + 44 23h + h2 = 0 + 44 Combine like terms: 0 + 44 = 44 23h + h2 = 44 The h term is 23h. Take half its coefficient (11.5). Square it (132.25) and add it to both sides. Add '132.25' to each side of the equation. 23h + 132.25 + h2 = 44 + 132.25 Reorder the terms: 132.25 + 23h + h2 = 44 + 132.25 Combine like terms: 44 + 132.25 = 176.25 132.25 + 23h + h2 = 176.25 Factor a perfect square on the left side: (h + 11.5)(h + 11.5) = 176.25 Calculate the square root of the right side: 13.275918047 Break this problem into two subproblems by setting (h + 11.5) equal to 13.275918047 and -13.275918047.Subproblem 1
h + 11.5 = 13.275918047 Simplifying h + 11.5 = 13.275918047 Reorder the terms: 11.5 + h = 13.275918047 Solving 11.5 + h = 13.275918047 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + h = 13.275918047 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + h = 13.275918047 + -11.5 h = 13.275918047 + -11.5 Combine like terms: 13.275918047 + -11.5 = 1.775918047 h = 1.775918047 Simplifying h = 1.775918047Subproblem 2
h + 11.5 = -13.275918047 Simplifying h + 11.5 = -13.275918047 Reorder the terms: 11.5 + h = -13.275918047 Solving 11.5 + h = -13.275918047 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-11.5' to each side of the equation. 11.5 + -11.5 + h = -13.275918047 + -11.5 Combine like terms: 11.5 + -11.5 = 0.0 0.0 + h = -13.275918047 + -11.5 h = -13.275918047 + -11.5 Combine like terms: -13.275918047 + -11.5 = -24.775918047 h = -24.775918047 Simplifying h = -24.775918047Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.775918047, -24.775918047}
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