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Simplifying 3y2 + -2.55y + -1.0 = 0.5 Reorder the terms: -1.0 + -2.55y + 3y2 = 0.5 Solving -1.0 + -2.55y + 3y2 = 0.5 Solving for variable 'y'. Reorder the terms: -1.0 + -0.5 + -2.55y + 3y2 = 0.5 + -0.5 Combine like terms: -1.0 + -0.5 = -1.5 -1.5 + -2.55y + 3y2 = 0.5 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 -1.5 + -2.55y + 3y2 = 0.0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -0.5 + -0.85y + y2 = 0.0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.85y + 0.5 + y2 = 0.0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.85y + y2 = 0.0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.85y + y2 = 0.0 + 0.5 -0.85y + y2 = 0.0 + 0.5 Combine like terms: 0.0 + 0.5 = 0.5 -0.85y + y2 = 0.5 The y term is -0.85y. Take half its coefficient (-0.425). Square it (0.180625) and add it to both sides. Add '0.180625' to each side of the equation. -0.85y + 0.180625 + y2 = 0.5 + 0.180625 Reorder the terms: 0.180625 + -0.85y + y2 = 0.5 + 0.180625 Combine like terms: 0.5 + 0.180625 = 0.680625 0.180625 + -0.85y + y2 = 0.680625 Factor a perfect square on the left side: (y + -0.425)(y + -0.425) = 0.680625 Calculate the square root of the right side: 0.825 Break this problem into two subproblems by setting (y + -0.425) equal to 0.825 and -0.825.Subproblem 1
y + -0.425 = 0.825 Simplifying y + -0.425 = 0.825 Reorder the terms: -0.425 + y = 0.825 Solving -0.425 + y = 0.825 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + y = 0.825 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + y = 0.825 + 0.425 y = 0.825 + 0.425 Combine like terms: 0.825 + 0.425 = 1.25 y = 1.25 Simplifying y = 1.25Subproblem 2
y + -0.425 = -0.825 Simplifying y + -0.425 = -0.825 Reorder the terms: -0.425 + y = -0.825 Solving -0.425 + y = -0.825 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.425' to each side of the equation. -0.425 + 0.425 + y = -0.825 + 0.425 Combine like terms: -0.425 + 0.425 = 0.000 0.000 + y = -0.825 + 0.425 y = -0.825 + 0.425 Combine like terms: -0.825 + 0.425 = -0.4 y = -0.4 Simplifying y = -0.4Solution
The solution to the problem is based on the solutions from the subproblems. y = {1.25, -0.4}
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