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Simplifying 3h2 + 30h = 39 Reorder the terms: 30h + 3h2 = 39 Solving 30h + 3h2 = 39 Solving for variable 'h'. Reorder the terms: -39 + 30h + 3h2 = 39 + -39 Combine like terms: 39 + -39 = 0 -39 + 30h + 3h2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-13 + 10h + h2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-13 + 10h + h2)' equal to zero and attempt to solve: Simplifying -13 + 10h + h2 = 0 Solving -13 + 10h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + 10h + 13 + h2 = 0 + 13 Reorder the terms: -13 + 13 + 10h + h2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + 10h + h2 = 0 + 13 10h + h2 = 0 + 13 Combine like terms: 0 + 13 = 13 10h + h2 = 13 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 = 13 + 25 Reorder the terms: 25 + 10h + h2 = 13 + 25 Combine like terms: 13 + 25 = 38 25 + 10h + h2 = 38 Factor a perfect square on the left side: (h + 5)(h + 5) = 38 Calculate the square root of the right side: 6.164414003 Break this problem into two subproblems by setting (h + 5) equal to 6.164414003 and -6.164414003.Subproblem 1
h + 5 = 6.164414003 Simplifying h + 5 = 6.164414003 Reorder the terms: 5 + h = 6.164414003 Solving 5 + h = 6.164414003 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 = 6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + h = 6.164414003 + -5 h = 6.164414003 + -5 Combine like terms: 6.164414003 + -5 = 1.164414003 h = 1.164414003 Simplifying h = 1.164414003Subproblem 2
h + 5 = -6.164414003 Simplifying h + 5 = -6.164414003 Reorder the terms: 5 + h = -6.164414003 Solving 5 + h = -6.164414003 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 = -6.164414003 + -5 Combine like terms: 5 + -5 = 0 0 + h = -6.164414003 + -5 h = -6.164414003 + -5 Combine like terms: -6.164414003 + -5 = -11.164414003 h = -11.164414003 Simplifying h = -11.164414003Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.164414003, -11.164414003}Solution
h = {1.164414003, -11.164414003}
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