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Simplifying h2 + -40h + 218 = 0 Reorder the terms: 218 + -40h + h2 = 0 Solving 218 + -40h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-218' to each side of the equation. 218 + -40h + -218 + h2 = 0 + -218 Reorder the terms: 218 + -218 + -40h + h2 = 0 + -218 Combine like terms: 218 + -218 = 0 0 + -40h + h2 = 0 + -218 -40h + h2 = 0 + -218 Combine like terms: 0 + -218 = -218 -40h + h2 = -218 The h term is -40h. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40h + 400 + h2 = -218 + 400 Reorder the terms: 400 + -40h + h2 = -218 + 400 Combine like terms: -218 + 400 = 182 400 + -40h + h2 = 182 Factor a perfect square on the left side: (h + -20)(h + -20) = 182 Calculate the square root of the right side: 13.490737563 Break this problem into two subproblems by setting (h + -20) equal to 13.490737563 and -13.490737563.Subproblem 1
h + -20 = 13.490737563 Simplifying h + -20 = 13.490737563 Reorder the terms: -20 + h = 13.490737563 Solving -20 + h = 13.490737563 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + h = 13.490737563 + 20 Combine like terms: -20 + 20 = 0 0 + h = 13.490737563 + 20 h = 13.490737563 + 20 Combine like terms: 13.490737563 + 20 = 33.490737563 h = 33.490737563 Simplifying h = 33.490737563Subproblem 2
h + -20 = -13.490737563 Simplifying h + -20 = -13.490737563 Reorder the terms: -20 + h = -13.490737563 Solving -20 + h = -13.490737563 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + h = -13.490737563 + 20 Combine like terms: -20 + 20 = 0 0 + h = -13.490737563 + 20 h = -13.490737563 + 20 Combine like terms: -13.490737563 + 20 = 6.509262437 h = 6.509262437 Simplifying h = 6.509262437Solution
The solution to the problem is based on the solutions from the subproblems. h = {33.490737563, 6.509262437}
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