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Simplifying y2 + -20y = -73 Reorder the terms: -20y + y2 = -73 Solving -20y + y2 = -73 Solving for variable 'y'. Reorder the terms: 73 + -20y + y2 = -73 + 73 Combine like terms: -73 + 73 = 0 73 + -20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-73' to each side of the equation. 73 + -20y + -73 + y2 = 0 + -73 Reorder the terms: 73 + -73 + -20y + y2 = 0 + -73 Combine like terms: 73 + -73 = 0 0 + -20y + y2 = 0 + -73 -20y + y2 = 0 + -73 Combine like terms: 0 + -73 = -73 -20y + y2 = -73 The y term is -20y. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20y + 100 + y2 = -73 + 100 Reorder the terms: 100 + -20y + y2 = -73 + 100 Combine like terms: -73 + 100 = 27 100 + -20y + y2 = 27 Factor a perfect square on the left side: (y + -10)(y + -10) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (y + -10) equal to 5.196152423 and -5.196152423.Subproblem 1
y + -10 = 5.196152423 Simplifying y + -10 = 5.196152423 Reorder the terms: -10 + y = 5.196152423 Solving -10 + y = 5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = 5.196152423 + 10 Combine like terms: -10 + 10 = 0 0 + y = 5.196152423 + 10 y = 5.196152423 + 10 Combine like terms: 5.196152423 + 10 = 15.196152423 y = 15.196152423 Simplifying y = 15.196152423Subproblem 2
y + -10 = -5.196152423 Simplifying y + -10 = -5.196152423 Reorder the terms: -10 + y = -5.196152423 Solving -10 + y = -5.196152423 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + y = -5.196152423 + 10 Combine like terms: -10 + 10 = 0 0 + y = -5.196152423 + 10 y = -5.196152423 + 10 Combine like terms: -5.196152423 + 10 = 4.803847577 y = 4.803847577 Simplifying y = 4.803847577Solution
The solution to the problem is based on the solutions from the subproblems. y = {15.196152423, 4.803847577}
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