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Simplifying 36h2 + -108h + 43 = 0 Reorder the terms: 43 + -108h + 36h2 = 0 Solving 43 + -108h + 36h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. 1.194444444 + -3h + h2 = 0 Move the constant term to the right: Add '-1.194444444' to each side of the equation. 1.194444444 + -3h + -1.194444444 + h2 = 0 + -1.194444444 Reorder the terms: 1.194444444 + -1.194444444 + -3h + h2 = 0 + -1.194444444 Combine like terms: 1.194444444 + -1.194444444 = 0.000000000 0.000000000 + -3h + h2 = 0 + -1.194444444 -3h + h2 = 0 + -1.194444444 Combine like terms: 0 + -1.194444444 = -1.194444444 -3h + h2 = -1.194444444 The h term is -3h. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3h + 2.25 + h2 = -1.194444444 + 2.25 Reorder the terms: 2.25 + -3h + h2 = -1.194444444 + 2.25 Combine like terms: -1.194444444 + 2.25 = 1.055555556 2.25 + -3h + h2 = 1.055555556 Factor a perfect square on the left side: (h + -1.5)(h + -1.5) = 1.055555556 Calculate the square root of the right side: 1.027402334 Break this problem into two subproblems by setting (h + -1.5) equal to 1.027402334 and -1.027402334.Subproblem 1
h + -1.5 = 1.027402334 Simplifying h + -1.5 = 1.027402334 Reorder the terms: -1.5 + h = 1.027402334 Solving -1.5 + h = 1.027402334 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + h = 1.027402334 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = 1.027402334 + 1.5 h = 1.027402334 + 1.5 Combine like terms: 1.027402334 + 1.5 = 2.527402334 h = 2.527402334 Simplifying h = 2.527402334Subproblem 2
h + -1.5 = -1.027402334 Simplifying h + -1.5 = -1.027402334 Reorder the terms: -1.5 + h = -1.027402334 Solving -1.5 + h = -1.027402334 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + h = -1.027402334 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + h = -1.027402334 + 1.5 h = -1.027402334 + 1.5 Combine like terms: -1.027402334 + 1.5 = 0.472597666 h = 0.472597666 Simplifying h = 0.472597666Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.527402334, 0.472597666}
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