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Simplifying y2 + -20y = 4 Reorder the terms: -20y + y2 = 4 Solving -20y + y2 = 4 Solving for variable 'y'. Reorder the terms: -4 + -20y + y2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -20y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -20y + 4 + y2 = 0 + 4 Reorder the terms: -4 + 4 + -20y + y2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -20y + y2 = 0 + 4 -20y + y2 = 0 + 4 Combine like terms: 0 + 4 = 4 -20y + y2 = 4 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 = 4 + 100 Reorder the terms: 100 + -20y + y2 = 4 + 100 Combine like terms: 4 + 100 = 104 100 + -20y + y2 = 104 Factor a perfect square on the left side: (y + -10)(y + -10) = 104 Calculate the square root of the right side: 10.198039027 Break this problem into two subproblems by setting (y + -10) equal to 10.198039027 and -10.198039027.Subproblem 1
y + -10 = 10.198039027 Simplifying y + -10 = 10.198039027 Reorder the terms: -10 + y = 10.198039027 Solving -10 + y = 10.198039027 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 = 10.198039027 + 10 Combine like terms: -10 + 10 = 0 0 + y = 10.198039027 + 10 y = 10.198039027 + 10 Combine like terms: 10.198039027 + 10 = 20.198039027 y = 20.198039027 Simplifying y = 20.198039027Subproblem 2
y + -10 = -10.198039027 Simplifying y + -10 = -10.198039027 Reorder the terms: -10 + y = -10.198039027 Solving -10 + y = -10.198039027 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 = -10.198039027 + 10 Combine like terms: -10 + 10 = 0 0 + y = -10.198039027 + 10 y = -10.198039027 + 10 Combine like terms: -10.198039027 + 10 = -0.198039027 y = -0.198039027 Simplifying y = -0.198039027Solution
The solution to the problem is based on the solutions from the subproblems. y = {20.198039027, -0.198039027}
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