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Simplifying 0 = -8 + -3y + y2 Solving 0 = -8 + -3y + y2 Solving for variable 'y'. Combine like terms: 0 + 8 = 8 8 + 3y + -1y2 = -8 + -3y + y2 + 8 + 3y + -1y2 Reorder the terms: 8 + 3y + -1y2 = -8 + 8 + -3y + 3y + y2 + -1y2 Combine like terms: -8 + 8 = 0 8 + 3y + -1y2 = 0 + -3y + 3y + y2 + -1y2 8 + 3y + -1y2 = -3y + 3y + y2 + -1y2 Combine like terms: -3y + 3y = 0 8 + 3y + -1y2 = 0 + y2 + -1y2 8 + 3y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 8 + 3y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -8 + -3y + y2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -3y + 8 + y2 = 0 + 8 Reorder the terms: -8 + 8 + -3y + y2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3y + y2 = 0 + 8 -3y + y2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3y + y2 = 8 The y term is -3y. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3y + 2.25 + y2 = 8 + 2.25 Reorder the terms: 2.25 + -3y + y2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3y + y2 = 10.25 Factor a perfect square on the left side: (y + -1.5)(y + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (y + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
y + -1.5 = 3.201562119 Simplifying y + -1.5 = 3.201562119 Reorder the terms: -1.5 + y = 3.201562119 Solving -1.5 + y = 3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = 3.201562119 + 1.5 y = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 y = 4.701562119 Simplifying y = 4.701562119Subproblem 2
y + -1.5 = -3.201562119 Simplifying y + -1.5 = -3.201562119 Reorder the terms: -1.5 + y = -3.201562119 Solving -1.5 + y = -3.201562119 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + y = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + y = -3.201562119 + 1.5 y = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 y = -1.701562119 Simplifying y = -1.701562119Solution
The solution to the problem is based on the solutions from the subproblems. y = {4.701562119, -1.701562119}
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