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Simplifying 3y + 6 = y2 Reorder the terms: 6 + 3y = y2 Solving 6 + 3y = y2 Solving for variable 'y'. Combine like terms: y2 + -1y2 = 0 6 + 3y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6 + -3y + y2 = 0 Move the constant term to the right: Add '6' to each side of the equation. -6 + -3y + 6 + y2 = 0 + 6 Reorder the terms: -6 + 6 + -3y + y2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -3y + y2 = 0 + 6 -3y + y2 = 0 + 6 Combine like terms: 0 + 6 = 6 -3y + y2 = 6 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 6 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 6 + 2.25 Combine like terms: 6 + 2.25 = 8.25 2.25 + -3y + y2 = 8.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (y + -1.5) equal to 2.872281323 and -2.872281323.Subproblem 1
y + -1.5 = 2.872281323 Simplifying y + -1.5 = 2.872281323 Reorder the terms: -1.5 + y = 2.872281323 Solving -1.5 + y = 2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 2.872281323 + 1.5 y = 2.872281323 + 1.5 Combine like terms: 2.872281323 + 1.5 = 4.372281323 y = 4.372281323 Simplifying y = 4.372281323Subproblem 2
y + -1.5 = -2.872281323 Simplifying y + -1.5 = -2.872281323 Reorder the terms: -1.5 + y = -2.872281323 Solving -1.5 + y = -2.872281323 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -2.872281323 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -2.872281323 + 1.5 y = -2.872281323 + 1.5 Combine like terms: -2.872281323 + 1.5 = -1.372281323 y = -1.372281323 Simplifying y = -1.372281323Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.372281323, -1.372281323}
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