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Simplifying -3h2 + 30h + 141 = 0 Reorder the terms: 141 + 30h + -3h2 = 0 Solving 141 + 30h + -3h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '3'. 3(47 + 10h + -1h2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(47 + 10h + -1h2)' equal to zero and attempt to solve: Simplifying 47 + 10h + -1h2 = 0 Solving 47 + 10h + -1h2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -47 + -10h + h2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + -10h + 47 + h2 = 0 + 47 Reorder the terms: -47 + 47 + -10h + h2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -10h + h2 = 0 + 47 -10h + h2 = 0 + 47 Combine like terms: 0 + 47 = 47 -10h + h2 = 47 The h term is -10h. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10h + 25 + h2 = 47 + 25 Reorder the terms: 25 + -10h + h2 = 47 + 25 Combine like terms: 47 + 25 = 72 25 + -10h + h2 = 72 Factor a perfect square on the left side: (h + -5)(h + -5) = 72 Calculate the square root of the right side: 8.485281374 Break this problem into two subproblems by setting (h + -5) equal to 8.485281374 and -8.485281374.Subproblem 1
h + -5 = 8.485281374 Simplifying h + -5 = 8.485281374 Reorder the terms: -5 + h = 8.485281374 Solving -5 + h = 8.485281374 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + h = 8.485281374 + 5 Combine like terms: -5 + 5 = 0 0 + h = 8.485281374 + 5 h = 8.485281374 + 5 Combine like terms: 8.485281374 + 5 = 13.485281374 h = 13.485281374 Simplifying h = 13.485281374Subproblem 2
h + -5 = -8.485281374 Simplifying h + -5 = -8.485281374 Reorder the terms: -5 + h = -8.485281374 Solving -5 + h = -8.485281374 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + h = -8.485281374 + 5 Combine like terms: -5 + 5 = 0 0 + h = -8.485281374 + 5 h = -8.485281374 + 5 Combine like terms: -8.485281374 + 5 = -3.485281374 h = -3.485281374 Simplifying h = -3.485281374Solution
The solution to the problem is based on the solutions from the subproblems. h = {13.485281374, -3.485281374}Solution
h = {13.485281374, -3.485281374}
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