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Simplifying 2h2 + 6h + -28 = 0 Reorder the terms: -28 + 6h + 2h2 = 0 Solving -28 + 6h + 2h2 = 0 Solving for variable 'h'. Factor out the Greatest Common Factor (GCF), '2'. 2(-14 + 3h + h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-14 + 3h + h2)' equal to zero and attempt to solve: Simplifying -14 + 3h + h2 = 0 Solving -14 + 3h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '14' to each side of the equation. -14 + 3h + 14 + h2 = 0 + 14 Reorder the terms: -14 + 14 + 3h + h2 = 0 + 14 Combine like terms: -14 + 14 = 0 0 + 3h + h2 = 0 + 14 3h + h2 = 0 + 14 Combine like terms: 0 + 14 = 14 3h + h2 = 14 The h term is 3h. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3h + 2.25 + h2 = 14 + 2.25 Reorder the terms: 2.25 + 3h + h2 = 14 + 2.25 Combine like terms: 14 + 2.25 = 16.25 2.25 + 3h + h2 = 16.25 Factor a perfect square on the left side: (h + 1.5)(h + 1.5) = 16.25 Calculate the square root of the right side: 4.031128874 Break this problem into two subproblems by setting (h + 1.5) equal to 4.031128874 and -4.031128874.Subproblem 1
h + 1.5 = 4.031128874 Simplifying h + 1.5 = 4.031128874 Reorder the terms: 1.5 + h = 4.031128874 Solving 1.5 + h = 4.031128874 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = 4.031128874 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = 4.031128874 + -1.5 h = 4.031128874 + -1.5 Combine like terms: 4.031128874 + -1.5 = 2.531128874 h = 2.531128874 Simplifying h = 2.531128874Subproblem 2
h + 1.5 = -4.031128874 Simplifying h + 1.5 = -4.031128874 Reorder the terms: 1.5 + h = -4.031128874 Solving 1.5 + h = -4.031128874 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + h = -4.031128874 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + h = -4.031128874 + -1.5 h = -4.031128874 + -1.5 Combine like terms: -4.031128874 + -1.5 = -5.531128874 h = -5.531128874 Simplifying h = -5.531128874Solution
The solution to the problem is based on the solutions from the subproblems. h = {2.531128874, -5.531128874}Solution
h = {2.531128874, -5.531128874}
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