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Simplifying 27 + 2h + 2h2 = 29 Solving 27 + 2h + 2h2 = 29 Solving for variable 'h'. Reorder the terms: 27 + -29 + 2h + 2h2 = 29 + -29 Combine like terms: 27 + -29 = -2 -2 + 2h + 2h2 = 29 + -29 Combine like terms: 29 + -29 = 0 -2 + 2h + 2h2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1 + h + h2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + h + h2)' equal to zero and attempt to solve: Simplifying -1 + h + h2 = 0 Solving -1 + h + h2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + h + 1 + h2 = 0 + 1 Reorder the terms: -1 + 1 + h + h2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + h + h2 = 0 + 1 h + h2 = 0 + 1 Combine like terms: 0 + 1 = 1 h + h2 = 1 The h term is h. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. h + 0.25 + h2 = 1 + 0.25 Reorder the terms: 0.25 + h + h2 = 1 + 0.25 Combine like terms: 1 + 0.25 = 1.25 0.25 + h + h2 = 1.25 Factor a perfect square on the left side: (h + 0.5)(h + 0.5) = 1.25 Calculate the square root of the right side: 1.118033989 Break this problem into two subproblems by setting (h + 0.5) equal to 1.118033989 and -1.118033989.Subproblem 1
h + 0.5 = 1.118033989 Simplifying h + 0.5 = 1.118033989 Reorder the terms: 0.5 + h = 1.118033989 Solving 0.5 + h = 1.118033989 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + h = 1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = 1.118033989 + -0.5 h = 1.118033989 + -0.5 Combine like terms: 1.118033989 + -0.5 = 0.618033989 h = 0.618033989 Simplifying h = 0.618033989Subproblem 2
h + 0.5 = -1.118033989 Simplifying h + 0.5 = -1.118033989 Reorder the terms: 0.5 + h = -1.118033989 Solving 0.5 + h = -1.118033989 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + h = -1.118033989 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + h = -1.118033989 + -0.5 h = -1.118033989 + -0.5 Combine like terms: -1.118033989 + -0.5 = -1.618033989 h = -1.618033989 Simplifying h = -1.618033989Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.618033989, -1.618033989}Solution
h = {0.618033989, -1.618033989}
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