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Simplifying 12 = 3h2 + 6h + -4 Reorder the terms: 12 = -4 + 6h + 3h2 Solving 12 = -4 + 6h + 3h2 Solving for variable 'h'. Combine like terms: 12 + 4 = 16 16 + -6h + -3h2 = -4 + 6h + 3h2 + 4 + -6h + -3h2 Reorder the terms: 16 + -6h + -3h2 = -4 + 4 + 6h + -6h + 3h2 + -3h2 Combine like terms: -4 + 4 = 0 16 + -6h + -3h2 = 0 + 6h + -6h + 3h2 + -3h2 16 + -6h + -3h2 = 6h + -6h + 3h2 + -3h2 Combine like terms: 6h + -6h = 0 16 + -6h + -3h2 = 0 + 3h2 + -3h2 16 + -6h + -3h2 = 3h2 + -3h2 Combine like terms: 3h2 + -3h2 = 0 16 + -6h + -3h2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -5.333333333 + 2h + h2 = 0 Move the constant term to the right: Add '5.333333333' to each side of the equation. -5.333333333 + 2h + 5.333333333 + h2 = 0 + 5.333333333 Reorder the terms: -5.333333333 + 5.333333333 + 2h + h2 = 0 + 5.333333333 Combine like terms: -5.333333333 + 5.333333333 = 0.000000000 0.000000000 + 2h + h2 = 0 + 5.333333333 2h + h2 = 0 + 5.333333333 Combine like terms: 0 + 5.333333333 = 5.333333333 2h + h2 = 5.333333333 The h term is 2h. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2h + 1 + h2 = 5.333333333 + 1 Reorder the terms: 1 + 2h + h2 = 5.333333333 + 1 Combine like terms: 5.333333333 + 1 = 6.333333333 1 + 2h + h2 = 6.333333333 Factor a perfect square on the left side: (h + 1)(h + 1) = 6.333333333 Calculate the square root of the right side: 2.516611478 Break this problem into two subproblems by setting (h + 1) equal to 2.516611478 and -2.516611478.Subproblem 1
h + 1 = 2.516611478 Simplifying h + 1 = 2.516611478 Reorder the terms: 1 + h = 2.516611478 Solving 1 + h = 2.516611478 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = 2.516611478 + -1 Combine like terms: 1 + -1 = 0 0 + h = 2.516611478 + -1 h = 2.516611478 + -1 Combine like terms: 2.516611478 + -1 = 1.516611478 h = 1.516611478 Simplifying h = 1.516611478Subproblem 2
h + 1 = -2.516611478 Simplifying h + 1 = -2.516611478 Reorder the terms: 1 + h = -2.516611478 Solving 1 + h = -2.516611478 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + h = -2.516611478 + -1 Combine like terms: 1 + -1 = 0 0 + h = -2.516611478 + -1 h = -2.516611478 + -1 Combine like terms: -2.516611478 + -1 = -3.516611478 h = -3.516611478 Simplifying h = -3.516611478Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.516611478, -3.516611478}
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