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Simplifying 2h2 + -12h + -40 = 0 Reorder the terms: -40 + -12h + 2h2 = 0 Solving -40 + -12h + 2h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + -6h + h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-20 + -6h + h2)' equal to zero and attempt to solve: Simplifying -20 + -6h + h2 = 0 Solving -20 + -6h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + -6h + 20 + h2 = 0 + 20 Reorder the terms: -20 + 20 + -6h + h2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -6h + h2 = 0 + 20 -6h + h2 = 0 + 20 Combine like terms: 0 + 20 = 20 -6h + h2 = 20 The h term is -6h. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6h + 9 + h2 = 20 + 9 Reorder the terms: 9 + -6h + h2 = 20 + 9 Combine like terms: 20 + 9 = 29 9 + -6h + h2 = 29 Factor a perfect square on the left side: (h + -3)(h + -3) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (h + -3) equal to 5.385164807 and -5.385164807.Subproblem 1
h + -3 = 5.385164807 Simplifying h + -3 = 5.385164807 Reorder the terms: -3 + h = 5.385164807 Solving -3 + h = 5.385164807 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + h = 5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + h = 5.385164807 + 3 h = 5.385164807 + 3 Combine like terms: 5.385164807 + 3 = 8.385164807 h = 8.385164807 Simplifying h = 8.385164807Subproblem 2
h + -3 = -5.385164807 Simplifying h + -3 = -5.385164807 Reorder the terms: -3 + h = -5.385164807 Solving -3 + h = -5.385164807 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + h = -5.385164807 + 3 Combine like terms: -3 + 3 = 0 0 + h = -5.385164807 + 3 h = -5.385164807 + 3 Combine like terms: -5.385164807 + 3 = -2.385164807 h = -2.385164807 Simplifying h = -2.385164807Solution
The solution to the problem is based on the solutions from the subproblems. h = {8.385164807, -2.385164807}Solution
h = {8.385164807, -2.385164807}
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