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Simplifying y2 + -4.5y + -5 = 0 Reorder the terms: -5 + -4.5y + y2 = 0 Solving -5 + -4.5y + y2 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -4.5y + 5 + y2 = 0 + 5 Reorder the terms: -5 + 5 + -4.5y + y2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -4.5y + y2 = 0 + 5 -4.5y + y2 = 0 + 5 Combine like terms: 0 + 5 = 5 -4.5y + y2 = 5 The y term is -4.5y. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5y + 5.0625 + y2 = 5 + 5.0625 Reorder the terms: 5.0625 + -4.5y + y2 = 5 + 5.0625 Combine like terms: 5 + 5.0625 = 10.0625 5.0625 + -4.5y + y2 = 10.0625 Factor a perfect square on the left side: (y + -2.25)(y + -2.25) = 10.0625 Calculate the square root of the right side: 3.172144385 Break this problem into two subproblems by setting (y + -2.25) equal to 3.172144385 and -3.172144385.Subproblem 1
y + -2.25 = 3.172144385 Simplifying y + -2.25 = 3.172144385 Reorder the terms: -2.25 + y = 3.172144385 Solving -2.25 + y = 3.172144385 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = 3.172144385 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = 3.172144385 + 2.25 y = 3.172144385 + 2.25 Combine like terms: 3.172144385 + 2.25 = 5.422144385 y = 5.422144385 Simplifying y = 5.422144385Subproblem 2
y + -2.25 = -3.172144385 Simplifying y + -2.25 = -3.172144385 Reorder the terms: -2.25 + y = -3.172144385 Solving -2.25 + y = -3.172144385 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + y = -3.172144385 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + y = -3.172144385 + 2.25 y = -3.172144385 + 2.25 Combine like terms: -3.172144385 + 2.25 = -0.922144385 y = -0.922144385 Simplifying y = -0.922144385Solution
The solution to the problem is based on the solutions from the subproblems. y = {5.422144385, -0.922144385}
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