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Simplifying (y + 3)(y + -5) = 2y + -2 Reorder the terms: (3 + y)(y + -5) = 2y + -2 Reorder the terms: (3 + y)(-5 + y) = 2y + -2 Multiply (3 + y) * (-5 + y) (3(-5 + y) + y(-5 + y)) = 2y + -2 ((-5 * 3 + y * 3) + y(-5 + y)) = 2y + -2 ((-15 + 3y) + y(-5 + y)) = 2y + -2 (-15 + 3y + (-5 * y + y * y)) = 2y + -2 (-15 + 3y + (-5y + y2)) = 2y + -2 Combine like terms: 3y + -5y = -2y (-15 + -2y + y2) = 2y + -2 Reorder the terms: -15 + -2y + y2 = -2 + 2y Solving -15 + -2y + y2 = -2 + 2y Solving for variable 'y'. Reorder the terms: -15 + 2 + -2y + -2y + y2 = -2 + 2y + 2 + -2y Combine like terms: -15 + 2 = -13 -13 + -2y + -2y + y2 = -2 + 2y + 2 + -2y Combine like terms: -2y + -2y = -4y -13 + -4y + y2 = -2 + 2y + 2 + -2y Reorder the terms: -13 + -4y + y2 = -2 + 2 + 2y + -2y Combine like terms: -2 + 2 = 0 -13 + -4y + y2 = 0 + 2y + -2y -13 + -4y + y2 = 2y + -2y Combine like terms: 2y + -2y = 0 -13 + -4y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '13' to each side of the equation. -13 + -4y + 13 + y2 = 0 + 13 Reorder the terms: -13 + 13 + -4y + y2 = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -4y + y2 = 0 + 13 -4y + y2 = 0 + 13 Combine like terms: 0 + 13 = 13 -4y + y2 = 13 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 = 13 + 4 Reorder the terms: 4 + -4y + y2 = 13 + 4 Combine like terms: 13 + 4 = 17 4 + -4y + y2 = 17 Factor a perfect square on the left side: (y + -2)(y + -2) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (y + -2) equal to 4.123105626 and -4.123105626.Subproblem 1
y + -2 = 4.123105626 Simplifying y + -2 = 4.123105626 Reorder the terms: -2 + y = 4.123105626 Solving -2 + y = 4.123105626 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 = 4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + y = 4.123105626 + 2 y = 4.123105626 + 2 Combine like terms: 4.123105626 + 2 = 6.123105626 y = 6.123105626 Simplifying y = 6.123105626Subproblem 2
y + -2 = -4.123105626 Simplifying y + -2 = -4.123105626 Reorder the terms: -2 + y = -4.123105626 Solving -2 + y = -4.123105626 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 = -4.123105626 + 2 Combine like terms: -2 + 2 = 0 0 + y = -4.123105626 + 2 y = -4.123105626 + 2 Combine like terms: -4.123105626 + 2 = -2.123105626 y = -2.123105626 Simplifying y = -2.123105626Solution
The solution to the problem is based on the solutions from the subproblems. y = {6.123105626, -2.123105626}
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