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Simplifying 24y2 + -6y + -1 = 0 Reorder the terms: -1 + -6y + 24y2 = 0 Solving -1 + -6y + 24y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -0.04166666667 + -0.25y + y2 = 0 Move the constant term to the right: Add '0.04166666667' to each side of the equation. -0.04166666667 + -0.25y + 0.04166666667 + y2 = 0 + 0.04166666667 Reorder the terms: -0.04166666667 + 0.04166666667 + -0.25y + y2 = 0 + 0.04166666667 Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000 0.00000000000 + -0.25y + y2 = 0 + 0.04166666667 -0.25y + y2 = 0 + 0.04166666667 Combine like terms: 0 + 0.04166666667 = 0.04166666667 -0.25y + y2 = 0.04166666667 The y term is -0.25y. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25y + 0.015625 + y2 = 0.04166666667 + 0.015625 Reorder the terms: 0.015625 + -0.25y + y2 = 0.04166666667 + 0.015625 Combine like terms: 0.04166666667 + 0.015625 = 0.05729166667 0.015625 + -0.25y + y2 = 0.05729166667 Factor a perfect square on the left side: (y + -0.125)(y + -0.125) = 0.05729166667 Calculate the square root of the right side: 0.239356777 Break this problem into two subproblems by setting (y + -0.125) equal to 0.239356777 and -0.239356777.Subproblem 1
y + -0.125 = 0.239356777 Simplifying y + -0.125 = 0.239356777 Reorder the terms: -0.125 + y = 0.239356777 Solving -0.125 + y = 0.239356777 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = 0.239356777 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = 0.239356777 + 0.125 y = 0.239356777 + 0.125 Combine like terms: 0.239356777 + 0.125 = 0.364356777 y = 0.364356777 Simplifying y = 0.364356777Subproblem 2
y + -0.125 = -0.239356777 Simplifying y + -0.125 = -0.239356777 Reorder the terms: -0.125 + y = -0.239356777 Solving -0.125 + y = -0.239356777 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = -0.239356777 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = -0.239356777 + 0.125 y = -0.239356777 + 0.125 Combine like terms: -0.239356777 + 0.125 = -0.114356777 y = -0.114356777 Simplifying y = -0.114356777Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.364356777, -0.114356777}
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