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Simplifying y2 + -20y = 13 Reorder the terms: -20y + y2 = 13 Solving -20y + y2 = 13 Solving for variable 'y'. Reorder the terms: -13 + -20y + y2 = 13 + -13 Combine like terms: 13 + -13 = 0 -13 + -20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -20y + 13 + y2 = 0 + 13 Reorder the terms: -13 + 13 + -20y + y2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -20y + y2 = 0 + 13 -20y + y2 = 0 + 13 Combine like terms: 0 + 13 = 13 -20y + y2 = 13 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 = 13 + 100 Reorder the terms: 100 + -20y + y2 = 13 + 100 Combine like terms: 13 + 100 = 113 100 + -20y + y2 = 113 Factor a perfect square on the left side: (y + -10)(y + -10) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (y + -10) equal to 10.630145813 and -10.630145813.Subproblem 1
y + -10 = 10.630145813 Simplifying y + -10 = 10.630145813 Reorder the terms: -10 + y = 10.630145813 Solving -10 + y = 10.630145813 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 = 10.630145813 + 10 Combine like terms: -10 + 10 = 0 0 + y = 10.630145813 + 10 y = 10.630145813 + 10 Combine like terms: 10.630145813 + 10 = 20.630145813 y = 20.630145813 Simplifying y = 20.630145813Subproblem 2
y + -10 = -10.630145813 Simplifying y + -10 = -10.630145813 Reorder the terms: -10 + y = -10.630145813 Solving -10 + y = -10.630145813 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 = -10.630145813 + 10 Combine like terms: -10 + 10 = 0 0 + y = -10.630145813 + 10 y = -10.630145813 + 10 Combine like terms: -10.630145813 + 10 = -0.630145813 y = -0.630145813 Simplifying y = -0.630145813Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.630145813, -0.630145813}
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