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Simplifying h2 + 28h + -8 = 0 Reorder the terms: -8 + 28h + h2 = 0 Solving -8 + 28h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 28h + 8 + h2 = 0 + 8 Reorder the terms: -8 + 8 + 28h + h2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 28h + h2 = 0 + 8 28h + h2 = 0 + 8 Combine like terms: 0 + 8 = 8 28h + h2 = 8 The h term is 28h. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28h + 196 + h2 = 8 + 196 Reorder the terms: 196 + 28h + h2 = 8 + 196 Combine like terms: 8 + 196 = 204 196 + 28h + h2 = 204 Factor a perfect square on the left side: (h + 14)(h + 14) = 204 Calculate the square root of the right side: 14.282856857 Break this problem into two subproblems by setting (h + 14) equal to 14.282856857 and -14.282856857.Subproblem 1
h + 14 = 14.282856857 Simplifying h + 14 = 14.282856857 Reorder the terms: 14 + h = 14.282856857 Solving 14 + h = 14.282856857 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + h = 14.282856857 + -14 Combine like terms: 14 + -14 = 0 0 + h = 14.282856857 + -14 h = 14.282856857 + -14 Combine like terms: 14.282856857 + -14 = 0.282856857 h = 0.282856857 Simplifying h = 0.282856857Subproblem 2
h + 14 = -14.282856857 Simplifying h + 14 = -14.282856857 Reorder the terms: 14 + h = -14.282856857 Solving 14 + h = -14.282856857 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + h = -14.282856857 + -14 Combine like terms: 14 + -14 = 0 0 + h = -14.282856857 + -14 h = -14.282856857 + -14 Combine like terms: -14.282856857 + -14 = -28.282856857 h = -28.282856857 Simplifying h = -28.282856857Solution
The solution to the problem is based on the solutions from the subproblems. h = {0.282856857, -28.282856857}
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