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Simplifying (y + -3)(y + -3) = 2y2 + 2y + -12 Reorder the terms: (-3 + y)(y + -3) = 2y2 + 2y + -12 Reorder the terms: (-3 + y)(-3 + y) = 2y2 + 2y + -12 Multiply (-3 + y) * (-3 + y) (-3(-3 + y) + y(-3 + y)) = 2y2 + 2y + -12 ((-3 * -3 + y * -3) + y(-3 + y)) = 2y2 + 2y + -12 ((9 + -3y) + y(-3 + y)) = 2y2 + 2y + -12 (9 + -3y + (-3 * y + y * y)) = 2y2 + 2y + -12 (9 + -3y + (-3y + y2)) = 2y2 + 2y + -12 Combine like terms: -3y + -3y = -6y (9 + -6y + y2) = 2y2 + 2y + -12 Reorder the terms: 9 + -6y + y2 = -12 + 2y + 2y2 Solving 9 + -6y + y2 = -12 + 2y + 2y2 Solving for variable 'y'. Reorder the terms: 9 + 12 + -6y + -2y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2 Combine like terms: 9 + 12 = 21 21 + -6y + -2y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2 Combine like terms: -6y + -2y = -8y 21 + -8y + y2 + -2y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2 Combine like terms: y2 + -2y2 = -1y2 21 + -8y + -1y2 = -12 + 2y + 2y2 + 12 + -2y + -2y2 Reorder the terms: 21 + -8y + -1y2 = -12 + 12 + 2y + -2y + 2y2 + -2y2 Combine like terms: -12 + 12 = 0 21 + -8y + -1y2 = 0 + 2y + -2y + 2y2 + -2y2 21 + -8y + -1y2 = 2y + -2y + 2y2 + -2y2 Combine like terms: 2y + -2y = 0 21 + -8y + -1y2 = 0 + 2y2 + -2y2 21 + -8y + -1y2 = 2y2 + -2y2 Combine like terms: 2y2 + -2y2 = 0 21 + -8y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -21 + 8y + y2 = 0 Move the constant term to the right: Add '21' to each side of the equation. -21 + 8y + 21 + y2 = 0 + 21 Reorder the terms: -21 + 21 + 8y + y2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + 8y + y2 = 0 + 21 8y + y2 = 0 + 21 Combine like terms: 0 + 21 = 21 8y + y2 = 21 The y term is 8y. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8y + 16 + y2 = 21 + 16 Reorder the terms: 16 + 8y + y2 = 21 + 16 Combine like terms: 21 + 16 = 37 16 + 8y + y2 = 37 Factor a perfect square on the left side: (y + 4)(y + 4) = 37 Calculate the square root of the right side: 6.08276253 Break this problem into two subproblems by setting (y + 4) equal to 6.08276253 and -6.08276253.Subproblem 1
y + 4 = 6.08276253 Simplifying y + 4 = 6.08276253 Reorder the terms: 4 + y = 6.08276253 Solving 4 + y = 6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = 6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + y = 6.08276253 + -4 y = 6.08276253 + -4 Combine like terms: 6.08276253 + -4 = 2.08276253 y = 2.08276253 Simplifying y = 2.08276253Subproblem 2
y + 4 = -6.08276253 Simplifying y + 4 = -6.08276253 Reorder the terms: 4 + y = -6.08276253 Solving 4 + y = -6.08276253 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + y = -6.08276253 + -4 Combine like terms: 4 + -4 = 0 0 + y = -6.08276253 + -4 y = -6.08276253 + -4 Combine like terms: -6.08276253 + -4 = -10.08276253 y = -10.08276253 Simplifying y = -10.08276253Solution
The solution to the problem is based on the solutions from the subproblems. y = {2.08276253, -10.08276253}
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