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Simplifying 3y2 = y2 + 9y + 1 Reorder the terms: 3y2 = 1 + 9y + y2 Solving 3y2 = 1 + 9y + y2 Solving for variable 'y'. Reorder the terms: -1 + -9y + 3y2 + -1y2 = 1 + 9y + y2 + -1 + -9y + -1y2 Combine like terms: 3y2 + -1y2 = 2y2 -1 + -9y + 2y2 = 1 + 9y + y2 + -1 + -9y + -1y2 Reorder the terms: -1 + -9y + 2y2 = 1 + -1 + 9y + -9y + y2 + -1y2 Combine like terms: 1 + -1 = 0 -1 + -9y + 2y2 = 0 + 9y + -9y + y2 + -1y2 -1 + -9y + 2y2 = 9y + -9y + y2 + -1y2 Combine like terms: 9y + -9y = 0 -1 + -9y + 2y2 = 0 + y2 + -1y2 -1 + -9y + 2y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 -1 + -9y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + -4.5y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -4.5y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -4.5y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -4.5y + y2 = 0 + 0.5 -4.5y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -4.5y + y2 = 0.5 The y term is -4.5y. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5y + 5.0625 + y2 = 0.5 + 5.0625 Reorder the terms: 5.0625 + -4.5y + y2 = 0.5 + 5.0625 Combine like terms: 0.5 + 5.0625 = 5.5625 5.0625 + -4.5y + y2 = 5.5625 Factor a perfect square on the left side: (y + -2.25)(y + -2.25) = 5.5625 Calculate the square root of the right side: 2.358495283 Break this problem into two subproblems by setting (y + -2.25) equal to 2.358495283 and -2.358495283.Subproblem 1
y + -2.25 = 2.358495283 Simplifying y + -2.25 = 2.358495283 Reorder the terms: -2.25 + y = 2.358495283 Solving -2.25 + y = 2.358495283 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = 2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = 2.358495283 + 2.25 y = 2.358495283 + 2.25 Combine like terms: 2.358495283 + 2.25 = 4.608495283 y = 4.608495283 Simplifying y = 4.608495283Subproblem 2
y + -2.25 = -2.358495283 Simplifying y + -2.25 = -2.358495283 Reorder the terms: -2.25 + y = -2.358495283 Solving -2.25 + y = -2.358495283 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = -2.358495283 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = -2.358495283 + 2.25 y = -2.358495283 + 2.25 Combine like terms: -2.358495283 + 2.25 = -0.108495283 y = -0.108495283 Simplifying y = -0.108495283Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.608495283, -0.108495283}
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