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Simplifying -4h2 + 76h = 200 Reorder the terms: 76h + -4h2 = 200 Solving 76h + -4h2 = 200 Solving for variable 'h'. Reorder the terms: -200 + 76h + -4h2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 76h + -4h2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-50 + 19h + -1h2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-50 + 19h + -1h2)' equal to zero and attempt to solve: Simplifying -50 + 19h + -1h2 = 0 Solving -50 + 19h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -19h + h2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -19h + -50 + h2 = 0 + -50 Reorder the terms: 50 + -50 + -19h + h2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -19h + h2 = 0 + -50 -19h + h2 = 0 + -50 Combine like terms: 0 + -50 = -50 -19h + h2 = -50 The h term is -19h. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19h + 90.25 + h2 = -50 + 90.25 Reorder the terms: 90.25 + -19h + h2 = -50 + 90.25 Combine like terms: -50 + 90.25 = 40.25 90.25 + -19h + h2 = 40.25 Factor a perfect square on the left side: (h + -9.5)(h + -9.5) = 40.25 Calculate the square root of the right side: 6.34428877 Break this problem into two subproblems by setting (h + -9.5) equal to 6.34428877 and -6.34428877.Subproblem 1
h + -9.5 = 6.34428877 Simplifying h + -9.5 = 6.34428877 Reorder the terms: -9.5 + h = 6.34428877 Solving -9.5 + h = 6.34428877 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + h = 6.34428877 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + h = 6.34428877 + 9.5 h = 6.34428877 + 9.5 Combine like terms: 6.34428877 + 9.5 = 15.84428877 h = 15.84428877 Simplifying h = 15.84428877Subproblem 2
h + -9.5 = -6.34428877 Simplifying h + -9.5 = -6.34428877 Reorder the terms: -9.5 + h = -6.34428877 Solving -9.5 + h = -6.34428877 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + h = -6.34428877 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + h = -6.34428877 + 9.5 h = -6.34428877 + 9.5 Combine like terms: -6.34428877 + 9.5 = 3.15571123 h = 3.15571123 Simplifying h = 3.15571123Solution
The solution to the problem is based on the solutions from the subproblems. h = {15.84428877, 3.15571123}Solution
h = {15.84428877, 3.15571123}
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