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Simplifying h2 + 20h + -26 = 0 Reorder the terms: -26 + 20h + h2 = 0 Solving -26 + 20h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + 20h + 26 + h2 = 0 + 26 Reorder the terms: -26 + 26 + 20h + h2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + 20h + h2 = 0 + 26 20h + h2 = 0 + 26 Combine like terms: 0 + 26 = 26 20h + h2 = 26 The h term is 20h. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20h + 100 + h2 = 26 + 100 Reorder the terms: 100 + 20h + h2 = 26 + 100 Combine like terms: 26 + 100 = 126 100 + 20h + h2 = 126 Factor a perfect square on the left side: (h + 10)(h + 10) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (h + 10) equal to 11.22497216 and -11.22497216.Subproblem 1
h + 10 = 11.22497216 Simplifying h + 10 = 11.22497216 Reorder the terms: 10 + h = 11.22497216 Solving 10 + h = 11.22497216 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = 11.22497216 + -10 Combine like terms: 10 + -10 = 0 0 + h = 11.22497216 + -10 h = 11.22497216 + -10 Combine like terms: 11.22497216 + -10 = 1.22497216 h = 1.22497216 Simplifying h = 1.22497216Subproblem 2
h + 10 = -11.22497216 Simplifying h + 10 = -11.22497216 Reorder the terms: 10 + h = -11.22497216 Solving 10 + h = -11.22497216 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + h = -11.22497216 + -10 Combine like terms: 10 + -10 = 0 0 + h = -11.22497216 + -10 h = -11.22497216 + -10 Combine like terms: -11.22497216 + -10 = -21.22497216 h = -21.22497216 Simplifying h = -21.22497216Solution
The solution to the problem is based on the solutions from the subproblems. h = {1.22497216, -21.22497216}
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