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Simplifying y2 + -1y + -130 = 0 Reorder the terms: -130 + -1y + y2 = 0 Solving -130 + -1y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '130' to each side of the equation. -130 + -1y + 130 + y2 = 0 + 130 Reorder the terms: -130 + 130 + -1y + y2 = 0 + 130 Combine like terms: -130 + 130 = 0 0 + -1y + y2 = 0 + 130 -1y + y2 = 0 + 130 Combine like terms: 0 + 130 = 130 -1y + y2 = 130 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 130 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 130 + 0.25 Combine like terms: 130 + 0.25 = 130.25 0.25 + -1y + y2 = 130.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (y + -0.5) equal to 11.412712211 and -11.412712211.Subproblem 1
y + -0.5 = 11.412712211 Simplifying y + -0.5 = 11.412712211 Reorder the terms: -0.5 + y = 11.412712211 Solving -0.5 + y = 11.412712211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 11.412712211 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 11.412712211 + 0.5 y = 11.412712211 + 0.5 Combine like terms: 11.412712211 + 0.5 = 11.912712211 y = 11.912712211 Simplifying y = 11.912712211Subproblem 2
y + -0.5 = -11.412712211 Simplifying y + -0.5 = -11.412712211 Reorder the terms: -0.5 + y = -11.412712211 Solving -0.5 + y = -11.412712211 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -11.412712211 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -11.412712211 + 0.5 y = -11.412712211 + 0.5 Combine like terms: -11.412712211 + 0.5 = -10.912712211 y = -10.912712211 Simplifying y = -10.912712211Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.912712211, -10.912712211}
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