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Simplifying -3y + 28 = y2 + 3y + -28 Reorder the terms: 28 + -3y = y2 + 3y + -28 Reorder the terms: 28 + -3y = -28 + 3y + y2 Solving 28 + -3y = -28 + 3y + y2 Solving for variable 'y'. Reorder the terms: 28 + 28 + -3y + -3y + -1y2 = -28 + 3y + y2 + 28 + -3y + -1y2 Combine like terms: 28 + 28 = 56 56 + -3y + -3y + -1y2 = -28 + 3y + y2 + 28 + -3y + -1y2 Combine like terms: -3y + -3y = -6y 56 + -6y + -1y2 = -28 + 3y + y2 + 28 + -3y + -1y2 Reorder the terms: 56 + -6y + -1y2 = -28 + 28 + 3y + -3y + y2 + -1y2 Combine like terms: -28 + 28 = 0 56 + -6y + -1y2 = 0 + 3y + -3y + y2 + -1y2 56 + -6y + -1y2 = 3y + -3y + y2 + -1y2 Combine like terms: 3y + -3y = 0 56 + -6y + -1y2 = 0 + y2 + -1y2 56 + -6y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 56 + -6y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -56 + 6y + y2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + 6y + 56 + y2 = 0 + 56 Reorder the terms: -56 + 56 + 6y + y2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 6y + y2 = 0 + 56 6y + y2 = 0 + 56 Combine like terms: 0 + 56 = 56 6y + y2 = 56 The y term is 6y. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6y + 9 + y2 = 56 + 9 Reorder the terms: 9 + 6y + y2 = 56 + 9 Combine like terms: 56 + 9 = 65 9 + 6y + y2 = 65 Factor a perfect square on the left side: (y + 3)(y + 3) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (y + 3) equal to 8.062257748 and -8.062257748.Subproblem 1
y + 3 = 8.062257748 Simplifying y + 3 = 8.062257748 Reorder the terms: 3 + y = 8.062257748 Solving 3 + y = 8.062257748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = 8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + y = 8.062257748 + -3 y = 8.062257748 + -3 Combine like terms: 8.062257748 + -3 = 5.062257748 y = 5.062257748 Simplifying y = 5.062257748Subproblem 2
y + 3 = -8.062257748 Simplifying y + 3 = -8.062257748 Reorder the terms: 3 + y = -8.062257748 Solving 3 + y = -8.062257748 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + y = -8.062257748 + -3 Combine like terms: 3 + -3 = 0 0 + y = -8.062257748 + -3 y = -8.062257748 + -3 Combine like terms: -8.062257748 + -3 = -11.062257748 y = -11.062257748 Simplifying y = -11.062257748Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.062257748, -11.062257748}
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