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Simplifying 6h2 + -11h + -3 = 0 Reorder the terms: -3 + -11h + 6h2 = 0 Solving -3 + -11h + 6h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -0.5 + -1.833333333h + h2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -1.833333333h + 0.5 + h2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -1.833333333h + h2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -1.833333333h + h2 = 0 + 0.5 -1.833333333h + h2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -1.833333333h + h2 = 0.5 The h term is -1.833333333h. Take half its coefficient (-0.9166666665). Square it (0.8402777775) and add it to both sides. Add '0.8402777775' to each side of the equation. -1.833333333h + 0.8402777775 + h2 = 0.5 + 0.8402777775 Reorder the terms: 0.8402777775 + -1.833333333h + h2 = 0.5 + 0.8402777775 Combine like terms: 0.5 + 0.8402777775 = 1.3402777775 0.8402777775 + -1.833333333h + h2 = 1.3402777775 Factor a perfect square on the left side: (h + -0.9166666665)(h + -0.9166666665) = 1.3402777775 Calculate the square root of the right side: 1.157703666 Break this problem into two subproblems by setting (h + -0.9166666665) equal to 1.157703666 and -1.157703666.Subproblem 1
h + -0.9166666665 = 1.157703666 Simplifying h + -0.9166666665 = 1.157703666 Reorder the terms: -0.9166666665 + h = 1.157703666 Solving -0.9166666665 + h = 1.157703666 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + h = 1.157703666 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + h = 1.157703666 + 0.9166666665 h = 1.157703666 + 0.9166666665 Combine like terms: 1.157703666 + 0.9166666665 = 2.0743703325 h = 2.0743703325 Simplifying h = 2.0743703325Subproblem 2
h + -0.9166666665 = -1.157703666 Simplifying h + -0.9166666665 = -1.157703666 Reorder the terms: -0.9166666665 + h = -1.157703666 Solving -0.9166666665 + h = -1.157703666 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '0.9166666665' to each side of the equation. -0.9166666665 + 0.9166666665 + h = -1.157703666 + 0.9166666665 Combine like terms: -0.9166666665 + 0.9166666665 = 0.0000000000 0.0000000000 + h = -1.157703666 + 0.9166666665 h = -1.157703666 + 0.9166666665 Combine like terms: -1.157703666 + 0.9166666665 = -0.2410369995 h = -0.2410369995 Simplifying h = -0.2410369995Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.0743703325, -0.2410369995}
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