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Simplifying 0.6h2 + -4.5h + -3 = 0 Reorder the terms: -3 + -4.5h + 0.6h2 = 0 Solving -3 + -4.5h + 0.6h2 = 0 Solving for variable 'h'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -5 + -7.5h + h2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -7.5h + 5 + h2 = 0 + 5 Reorder the terms: -5 + 5 + -7.5h + h2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -7.5h + h2 = 0 + 5 -7.5h + h2 = 0 + 5 Combine like terms: 0 + 5 = 5 -7.5h + h2 = 5 The h term is -7.5h. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5h + 14.0625 + h2 = 5 + 14.0625 Reorder the terms: 14.0625 + -7.5h + h2 = 5 + 14.0625 Combine like terms: 5 + 14.0625 = 19.0625 14.0625 + -7.5h + h2 = 19.0625 Factor a perfect square on the left side: (h + -3.75)(h + -3.75) = 19.0625 Calculate the square root of the right side: 4.366062299 Break this problem into two subproblems by setting (h + -3.75) equal to 4.366062299 and -4.366062299.Subproblem 1
h + -3.75 = 4.366062299 Simplifying h + -3.75 = 4.366062299 Reorder the terms: -3.75 + h = 4.366062299 Solving -3.75 + h = 4.366062299 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + h = 4.366062299 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + h = 4.366062299 + 3.75 h = 4.366062299 + 3.75 Combine like terms: 4.366062299 + 3.75 = 8.116062299 h = 8.116062299 Simplifying h = 8.116062299Subproblem 2
h + -3.75 = -4.366062299 Simplifying h + -3.75 = -4.366062299 Reorder the terms: -3.75 + h = -4.366062299 Solving -3.75 + h = -4.366062299 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + h = -4.366062299 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + h = -4.366062299 + 3.75 h = -4.366062299 + 3.75 Combine like terms: -4.366062299 + 3.75 = -0.616062299 h = -0.616062299 Simplifying h = -0.616062299Solution
The solution to the problem is based on the solutions from the subproblems. h = {8.116062299, -0.616062299}
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