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Simplifying 45y2 + -45y + -88 = 0 Reorder the terms: -88 + -45y + 45y2 = 0 Solving -88 + -45y + 45y2 = 0 Solving for variable 'y'. Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -1.955555556 + -1y + y2 = 0 Move the constant term to the right: Add '1.955555556' to each side of the equation. -1.955555556 + -1y + 1.955555556 + y2 = 0 + 1.955555556 Reorder the terms: -1.955555556 + 1.955555556 + -1y + y2 = 0 + 1.955555556 Combine like terms: -1.955555556 + 1.955555556 = 0.000000000 0.000000000 + -1y + y2 = 0 + 1.955555556 -1y + y2 = 0 + 1.955555556 Combine like terms: 0 + 1.955555556 = 1.955555556 -1y + y2 = 1.955555556 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = 1.955555556 + 0.25 Reorder the terms: 0.25 + -1y + y2 = 1.955555556 + 0.25 Combine like terms: 1.955555556 + 0.25 = 2.205555556 0.25 + -1y + y2 = 2.205555556 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = 2.205555556 Calculate the square root of the right side: 1.485111294 Break this problem into two subproblems by setting (y + -0.5) equal to 1.485111294 and -1.485111294.Subproblem 1
y + -0.5 = 1.485111294 Simplifying y + -0.5 = 1.485111294 Reorder the terms: -0.5 + y = 1.485111294 Solving -0.5 + y = 1.485111294 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = 1.485111294 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = 1.485111294 + 0.5 y = 1.485111294 + 0.5 Combine like terms: 1.485111294 + 0.5 = 1.985111294 y = 1.985111294 Simplifying y = 1.985111294Subproblem 2
y + -0.5 = -1.485111294 Simplifying y + -0.5 = -1.485111294 Reorder the terms: -0.5 + y = -1.485111294 Solving -0.5 + y = -1.485111294 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + y = -1.485111294 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + y = -1.485111294 + 0.5 y = -1.485111294 + 0.5 Combine like terms: -1.485111294 + 0.5 = -0.985111294 y = -0.985111294 Simplifying y = -0.985111294Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.985111294, -0.985111294}
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