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Simplifying h2 + -20h + 73 = 0 Reorder the terms: 73 + -20h + h2 = 0 Solving 73 + -20h + h2 = 0 Solving for variable 'h'. Begin completing the square. Move the constant term to the right: Add '-73' to each side of the equation. 73 + -20h + -73 + h2 = 0 + -73 Reorder the terms: 73 + -73 + -20h + h2 = 0 + -73 Combine like terms: 73 + -73 = 0 0 + -20h + h2 = 0 + -73 -20h + h2 = 0 + -73 Combine like terms: 0 + -73 = -73 -20h + h2 = -73 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 = -73 + 100 Reorder the terms: 100 + -20h + h2 = -73 + 100 Combine like terms: -73 + 100 = 27 100 + -20h + h2 = 27 Factor a perfect square on the left side: (h + -10)(h + -10) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (h + -10) equal to 5.196152423 and -5.196152423.Subproblem 1
h + -10 = 5.196152423 Simplifying h + -10 = 5.196152423 Reorder the terms: -10 + h = 5.196152423 Solving -10 + h = 5.196152423 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 = 5.196152423 + 10 Combine like terms: -10 + 10 = 0 0 + h = 5.196152423 + 10 h = 5.196152423 + 10 Combine like terms: 5.196152423 + 10 = 15.196152423 h = 15.196152423 Simplifying h = 15.196152423Subproblem 2
h + -10 = -5.196152423 Simplifying h + -10 = -5.196152423 Reorder the terms: -10 + h = -5.196152423 Solving -10 + h = -5.196152423 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 = -5.196152423 + 10 Combine like terms: -10 + 10 = 0 0 + h = -5.196152423 + 10 h = -5.196152423 + 10 Combine like terms: -5.196152423 + 10 = 4.803847577 h = 4.803847577 Simplifying h = 4.803847577Solution
The solution to the problem is based on the solutions from the subproblems. h = {15.196152423, 4.803847577}
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