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Simplifying 0 = 0.5y2 + -3.5y + -22 Reorder the terms: 0 = -22 + -3.5y + 0.5y2 Solving 0 = -22 + -3.5y + 0.5y2 Solving for variable 'y'. Combine like terms: 0 + 22 = 22 22 + 3.5y + -0.5y2 = -22 + -3.5y + 0.5y2 + 22 + 3.5y + -0.5y2 Reorder the terms: 22 + 3.5y + -0.5y2 = -22 + 22 + -3.5y + 3.5y + 0.5y2 + -0.5y2 Combine like terms: -22 + 22 = 0 22 + 3.5y + -0.5y2 = 0 + -3.5y + 3.5y + 0.5y2 + -0.5y2 22 + 3.5y + -0.5y2 = -3.5y + 3.5y + 0.5y2 + -0.5y2 Combine like terms: -3.5y + 3.5y = 0.0 22 + 3.5y + -0.5y2 = 0.0 + 0.5y2 + -0.5y2 22 + 3.5y + -0.5y2 = 0.5y2 + -0.5y2 Combine like terms: 0.5y2 + -0.5y2 = 0.0 22 + 3.5y + -0.5y2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. -44 + -7y + y2 = 0 Move the constant term to the right: Add '44' to each side of the equation. -44 + -7y + 44 + y2 = 0 + 44 Reorder the terms: -44 + 44 + -7y + y2 = 0 + 44 Combine like terms: -44 + 44 = 0 0 + -7y + y2 = 0 + 44 -7y + y2 = 0 + 44 Combine like terms: 0 + 44 = 44 -7y + y2 = 44 The y term is -7y. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7y + 12.25 + y2 = 44 + 12.25 Reorder the terms: 12.25 + -7y + y2 = 44 + 12.25 Combine like terms: 44 + 12.25 = 56.25 12.25 + -7y + y2 = 56.25 Factor a perfect square on the left side: (y + -3.5)(y + -3.5) = 56.25 Calculate the square root of the right side: 7.5 Break this problem into two subproblems by setting (y + -3.5) equal to 7.5 and -7.5.Subproblem 1
y + -3.5 = 7.5 Simplifying y + -3.5 = 7.5 Reorder the terms: -3.5 + y = 7.5 Solving -3.5 + y = 7.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = 7.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = 7.5 + 3.5 y = 7.5 + 3.5 Combine like terms: 7.5 + 3.5 = 11 y = 11 Simplifying y = 11Subproblem 2
y + -3.5 = -7.5 Simplifying y + -3.5 = -7.5 Reorder the terms: -3.5 + y = -7.5 Solving -3.5 + y = -7.5 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + y = -7.5 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + y = -7.5 + 3.5 y = -7.5 + 3.5 Combine like terms: -7.5 + 3.5 = -4 y = -4 Simplifying y = -4Solution
The solution to the problem is based on the solutions from the subproblems. y = {11, -4}
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