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Simplifying h2 + 28h + -31 = 0 Reorder the terms: -31 + 28h + h2 = 0 Solving -31 + 28h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '31' to each side of the equation. -31 + 28h + 31 + h2 = 0 + 31 Reorder the terms: -31 + 31 + 28h + h2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 28h + h2 = 0 + 31 28h + h2 = 0 + 31 Combine like terms: 0 + 31 = 31 28h + h2 = 31 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 = 31 + 196 Reorder the terms: 196 + 28h + h2 = 31 + 196 Combine like terms: 31 + 196 = 227 196 + 28h + h2 = 227 Factor a perfect square on the left side: (h + 14)(h + 14) = 227 Calculate the square root of the right side: 15.066519173 Break this problem into two subproblems by setting (h + 14) equal to 15.066519173 and -15.066519173.Subproblem 1
h + 14 = 15.066519173 Simplifying h + 14 = 15.066519173 Reorder the terms: 14 + h = 15.066519173 Solving 14 + h = 15.066519173 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 = 15.066519173 + -14 Combine like terms: 14 + -14 = 0 0 + h = 15.066519173 + -14 h = 15.066519173 + -14 Combine like terms: 15.066519173 + -14 = 1.066519173 h = 1.066519173 Simplifying h = 1.066519173Subproblem 2
h + 14 = -15.066519173 Simplifying h + 14 = -15.066519173 Reorder the terms: 14 + h = -15.066519173 Solving 14 + h = -15.066519173 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 = -15.066519173 + -14 Combine like terms: 14 + -14 = 0 0 + h = -15.066519173 + -14 h = -15.066519173 + -14 Combine like terms: -15.066519173 + -14 = -29.066519173 h = -29.066519173 Simplifying h = -29.066519173Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.066519173, -29.066519173}
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