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Simplifying 4h2 + 6h + -133 = 0 Reorder the terms: -133 + 6h + 4h2 = 0 Solving -133 + 6h + 4h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -33.25 + 1.5h + h2 = 0 Move the constant term to the right: Add '33.25' to each side of the equation. -33.25 + 1.5h + 33.25 + h2 = 0 + 33.25 Reorder the terms: -33.25 + 33.25 + 1.5h + h2 = 0 + 33.25 Combine like terms: -33.25 + 33.25 = 0.00 0.00 + 1.5h + h2 = 0 + 33.25 1.5h + h2 = 0 + 33.25 Combine like terms: 0 + 33.25 = 33.25 1.5h + h2 = 33.25 The h term is 1.5h. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5h + 0.5625 + h2 = 33.25 + 0.5625 Reorder the terms: 0.5625 + 1.5h + h2 = 33.25 + 0.5625 Combine like terms: 33.25 + 0.5625 = 33.8125 0.5625 + 1.5h + h2 = 33.8125 Factor a perfect square on the left side: (h + 0.75)(h + 0.75) = 33.8125 Calculate the square root of the right side: 5.814851675 Break this problem into two subproblems by setting (h + 0.75) equal to 5.814851675 and -5.814851675.Subproblem 1
h + 0.75 = 5.814851675 Simplifying h + 0.75 = 5.814851675 Reorder the terms: 0.75 + h = 5.814851675 Solving 0.75 + h = 5.814851675 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + h = 5.814851675 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + h = 5.814851675 + -0.75 h = 5.814851675 + -0.75 Combine like terms: 5.814851675 + -0.75 = 5.064851675 h = 5.064851675 Simplifying h = 5.064851675Subproblem 2
h + 0.75 = -5.814851675 Simplifying h + 0.75 = -5.814851675 Reorder the terms: 0.75 + h = -5.814851675 Solving 0.75 + h = -5.814851675 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.75' to each side of the equation. 0.75 + -0.75 + h = -5.814851675 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + h = -5.814851675 + -0.75 h = -5.814851675 + -0.75 Combine like terms: -5.814851675 + -0.75 = -6.564851675 h = -6.564851675 Simplifying h = -6.564851675Solution
The solution to the problem is based on the solutions from the subproblems. h = {5.064851675, -6.564851675}
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