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Simplifying 3y2 + -2 = 2y2 + 4y + 5 Reorder the terms: -2 + 3y2 = 2y2 + 4y + 5 Reorder the terms: -2 + 3y2 = 5 + 4y + 2y2 Solving -2 + 3y2 = 5 + 4y + 2y2 Solving for variable 'y'. Reorder the terms: -2 + -5 + -4y + 3y2 + -2y2 = 5 + 4y + 2y2 + -5 + -4y + -2y2 Combine like terms: -2 + -5 = -7 -7 + -4y + 3y2 + -2y2 = 5 + 4y + 2y2 + -5 + -4y + -2y2 Combine like terms: 3y2 + -2y2 = 1y2 -7 + -4y + 1y2 = 5 + 4y + 2y2 + -5 + -4y + -2y2 Reorder the terms: -7 + -4y + 1y2 = 5 + -5 + 4y + -4y + 2y2 + -2y2 Combine like terms: 5 + -5 = 0 -7 + -4y + 1y2 = 0 + 4y + -4y + 2y2 + -2y2 -7 + -4y + 1y2 = 4y + -4y + 2y2 + -2y2 Combine like terms: 4y + -4y = 0 -7 + -4y + 1y2 = 0 + 2y2 + -2y2 -7 + -4y + 1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 -7 + -4y + 1y2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -4y + 7 + y2 = 0 + 7 Reorder the terms: -7 + 7 + -4y + y2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -4y + y2 = 0 + 7 -4y + y2 = 0 + 7 Combine like terms: 0 + 7 = 7 -4y + y2 = 7 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = 7 + 4 Reorder the terms: 4 + -4y + y2 = 7 + 4 Combine like terms: 7 + 4 = 11 4 + -4y + y2 = 11 Factor a perfect square on the left side: (y + -2)(y + -2) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (y + -2) equal to 3.31662479 and -3.31662479.Subproblem 1
y + -2 = 3.31662479 Simplifying y + -2 = 3.31662479 Reorder the terms: -2 + y = 3.31662479 Solving -2 + y = 3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = 3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + y = 3.31662479 + 2 y = 3.31662479 + 2 Combine like terms: 3.31662479 + 2 = 5.31662479 y = 5.31662479 Simplifying y = 5.31662479Subproblem 2
y + -2 = -3.31662479 Simplifying y + -2 = -3.31662479 Reorder the terms: -2 + y = -3.31662479 Solving -2 + y = -3.31662479 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + y = -3.31662479 + 2 Combine like terms: -2 + 2 = 0 0 + y = -3.31662479 + 2 y = -3.31662479 + 2 Combine like terms: -3.31662479 + 2 = -1.31662479 y = -1.31662479 Simplifying y = -1.31662479Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.31662479, -1.31662479}
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