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Simplifying -3h2 + -3h + 2 = 0 Reorder the terms: 2 + -3h + -3h2 = 0 Solving 2 + -3h + -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'. -0.6666666667 + h + h2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + h + 0.6666666667 + h2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + h + h2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + h + h2 = 0 + 0.6666666667 h + h2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 h + h2 = 0.6666666667 The h term is h. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + h2 = 0.6666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + h2 = 0.6666666667 + 0.25 Combine like terms: 0.6666666667 + 0.25 = 0.9166666667 1.25 + h2 = 0.9166666667 Factor a perfect square on the left side: (h + 0.5)(h + 0.5) = 0.9166666667 Calculate the square root of the right side: 0.957427108 Break this problem into two subproblems by setting (h + 0.5) equal to 0.957427108 and -0.957427108.Subproblem 1
h + 0.5 = 0.957427108 Simplifying h + 0.5 = 0.957427108 Reorder the terms: 0.5 + h = 0.957427108 Solving 0.5 + h = 0.957427108 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + h = 0.957427108 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = 0.957427108 + -0.5 h = 0.957427108 + -0.5 Combine like terms: 0.957427108 + -0.5 = 0.457427108 h = 0.457427108 Simplifying h = 0.457427108Subproblem 2
h + 0.5 = -0.957427108 Simplifying h + 0.5 = -0.957427108 Reorder the terms: 0.5 + h = -0.957427108 Solving 0.5 + h = -0.957427108 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + h = -0.957427108 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = -0.957427108 + -0.5 h = -0.957427108 + -0.5 Combine like terms: -0.957427108 + -0.5 = -1.457427108 h = -1.457427108 Simplifying h = -1.457427108Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.457427108, -1.457427108}
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