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Simplifying 12h2 + -60h + -75 = 0 Reorder the terms: -75 + -60h + 12h2 = 0 Solving -75 + -60h + 12h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3'. 3(-25 + -20h + 4h2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-25 + -20h + 4h2)' equal to zero and attempt to solve: Simplifying -25 + -20h + 4h2 = 0 Solving -25 + -20h + 4h2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + -5h + h2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -5h + 6.25 + h2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -5h + h2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -5h + h2 = 0 + 6.25 -5h + h2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -5h + h2 = 6.25 The h term is -5h. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5h + 6.25 + h2 = 6.25 + 6.25 Reorder the terms: 6.25 + -5h + h2 = 6.25 + 6.25 Combine like terms: 6.25 + 6.25 = 12.5 6.25 + -5h + h2 = 12.5 Factor a perfect square on the left side: (h + -2.5)(h + -2.5) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (h + -2.5) equal to 3.535533906 and -3.535533906.Subproblem 1
h + -2.5 = 3.535533906 Simplifying h + -2.5 = 3.535533906 Reorder the terms: -2.5 + h = 3.535533906 Solving -2.5 + h = 3.535533906 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + h = 3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + h = 3.535533906 + 2.5 h = 3.535533906 + 2.5 Combine like terms: 3.535533906 + 2.5 = 6.035533906 h = 6.035533906 Simplifying h = 6.035533906Subproblem 2
h + -2.5 = -3.535533906 Simplifying h + -2.5 = -3.535533906 Reorder the terms: -2.5 + h = -3.535533906 Solving -2.5 + h = -3.535533906 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + h = -3.535533906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + h = -3.535533906 + 2.5 h = -3.535533906 + 2.5 Combine like terms: -3.535533906 + 2.5 = -1.035533906 h = -1.035533906 Simplifying h = -1.035533906Solution
The solution to the problem is based on the solutions from the subproblems. h = {6.035533906, -1.035533906}Solution
h = {6.035533906, -1.035533906}
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