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Simplifying 3h2 + -30h + 38 = 0 Reorder the terms: 38 + -30h + 3h2 = 0 Solving 38 + -30h + 3h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 12.66666667 + -10h + h2 = 0 Move the constant term to the right: Add '-12.66666667' to each side of the equation. 12.66666667 + -10h + -12.66666667 + h2 = 0 + -12.66666667 Reorder the terms: 12.66666667 + -12.66666667 + -10h + h2 = 0 + -12.66666667 Combine like terms: 12.66666667 + -12.66666667 = 0.00000000 0.00000000 + -10h + h2 = 0 + -12.66666667 -10h + h2 = 0 + -12.66666667 Combine like terms: 0 + -12.66666667 = -12.66666667 -10h + h2 = -12.66666667 The h term is -10h. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10h + 25 + h2 = -12.66666667 + 25 Reorder the terms: 25 + -10h + h2 = -12.66666667 + 25 Combine like terms: -12.66666667 + 25 = 12.33333333 25 + -10h + h2 = 12.33333333 Factor a perfect square on the left side: (h + -5)(h + -5) = 12.33333333 Calculate the square root of the right side: 3.511884584 Break this problem into two subproblems by setting (h + -5) equal to 3.511884584 and -3.511884584.Subproblem 1
h + -5 = 3.511884584 Simplifying h + -5 = 3.511884584 Reorder the terms: -5 + h = 3.511884584 Solving -5 + h = 3.511884584 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + h = 3.511884584 + 5 Combine like terms: -5 + 5 = 0 0 + h = 3.511884584 + 5 h = 3.511884584 + 5 Combine like terms: 3.511884584 + 5 = 8.511884584 h = 8.511884584 Simplifying h = 8.511884584Subproblem 2
h + -5 = -3.511884584 Simplifying h + -5 = -3.511884584 Reorder the terms: -5 + h = -3.511884584 Solving -5 + h = -3.511884584 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + h = -3.511884584 + 5 Combine like terms: -5 + 5 = 0 0 + h = -3.511884584 + 5 h = -3.511884584 + 5 Combine like terms: -3.511884584 + 5 = 1.488115416 h = 1.488115416 Simplifying h = 1.488115416Solution
The solution to the problem is based on the solutions from the subproblems. h = {8.511884584, 1.488115416}
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