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Simplifying y2 + -1y + -58 = 0 Reorder the terms: -58 + -1y + y2 = 0 Solving -58 + -1y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '58' to each side of the equation. -58 + -1y + 58 + y2 = 0 + 58 Reorder the terms: -58 + 58 + -1y + y2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + -1y + y2 = 0 + 58 -1y + y2 = 0 + 58 Combine like terms: 0 + 58 = 58 -1y + y2 = 58 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 = 58 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 58 + 0.25 Combine like terms: 58 + 0.25 = 58.25 0.25 + -1y + y2 = 58.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 58.25 Calculate the square root of the right side: 7.632168761 Break this problem into two subproblems by setting (y + -0.5) equal to 7.632168761 and -7.632168761.Subproblem 1
y + -0.5 = 7.632168761 Simplifying y + -0.5 = 7.632168761 Reorder the terms: -0.5 + y = 7.632168761 Solving -0.5 + y = 7.632168761 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 = 7.632168761 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 7.632168761 + 0.5 y = 7.632168761 + 0.5 Combine like terms: 7.632168761 + 0.5 = 8.132168761 y = 8.132168761 Simplifying y = 8.132168761Subproblem 2
y + -0.5 = -7.632168761 Simplifying y + -0.5 = -7.632168761 Reorder the terms: -0.5 + y = -7.632168761 Solving -0.5 + y = -7.632168761 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 = -7.632168761 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -7.632168761 + 0.5 y = -7.632168761 + 0.5 Combine like terms: -7.632168761 + 0.5 = -7.132168761 y = -7.132168761 Simplifying y = -7.132168761Solution
The solution to the problem is based on the solutions from the subproblems. y = {8.132168761, -7.132168761}
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