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Simplifying 2y2 + -25y + 13 = 0 Reorder the terms: 13 + -25y + 2y2 = 0 Solving 13 + -25y + 2y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6.5 + -12.5y + y2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -12.5y + -6.5 + y2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -12.5y + y2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -12.5y + y2 = 0 + -6.5 -12.5y + y2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -12.5y + y2 = -6.5 The y term is -12.5y. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5y + 39.0625 + y2 = -6.5 + 39.0625 Reorder the terms: 39.0625 + -12.5y + y2 = -6.5 + 39.0625 Combine like terms: -6.5 + 39.0625 = 32.5625 39.0625 + -12.5y + y2 = 32.5625 Factor a perfect square on the left side: (y + -6.25)(y + -6.25) = 32.5625 Calculate the square root of the right side: 5.706356105 Break this problem into two subproblems by setting (y + -6.25) equal to 5.706356105 and -5.706356105.Subproblem 1
y + -6.25 = 5.706356105 Simplifying y + -6.25 = 5.706356105 Reorder the terms: -6.25 + y = 5.706356105 Solving -6.25 + y = 5.706356105 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + y = 5.706356105 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + y = 5.706356105 + 6.25 y = 5.706356105 + 6.25 Combine like terms: 5.706356105 + 6.25 = 11.956356105 y = 11.956356105 Simplifying y = 11.956356105Subproblem 2
y + -6.25 = -5.706356105 Simplifying y + -6.25 = -5.706356105 Reorder the terms: -6.25 + y = -5.706356105 Solving -6.25 + y = -5.706356105 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + y = -5.706356105 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + y = -5.706356105 + 6.25 y = -5.706356105 + 6.25 Combine like terms: -5.706356105 + 6.25 = 0.543643895 y = 0.543643895 Simplifying y = 0.543643895Solution
The solution to the problem is based on the solutions from the subproblems. y = {11.956356105, 0.543643895}
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