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Simplifying 4y2 + -1y = 2 Reorder the terms: -1y + 4y2 = 2 Solving -1y + 4y2 = 2 Solving for variable 'y'. Reorder the terms: -2 + -1y + 4y2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -1y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + -0.25y + y2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.25y + 0.5 + y2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.25y + y2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.25y + y2 = 0 + 0.5 -0.25y + y2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.25y + y2 = 0.5 The y term is -0.25y. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25y + 0.015625 + y2 = 0.5 + 0.015625 Reorder the terms: 0.015625 + -0.25y + y2 = 0.5 + 0.015625 Combine like terms: 0.5 + 0.015625 = 0.515625 0.015625 + -0.25y + y2 = 0.515625 Factor a perfect square on the left side: (y + -0.125)(y + -0.125) = 0.515625 Calculate the square root of the right side: 0.718070331 Break this problem into two subproblems by setting (y + -0.125) equal to 0.718070331 and -0.718070331.Subproblem 1
y + -0.125 = 0.718070331 Simplifying y + -0.125 = 0.718070331 Reorder the terms: -0.125 + y = 0.718070331 Solving -0.125 + y = 0.718070331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = 0.718070331 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = 0.718070331 + 0.125 y = 0.718070331 + 0.125 Combine like terms: 0.718070331 + 0.125 = 0.843070331 y = 0.843070331 Simplifying y = 0.843070331Subproblem 2
y + -0.125 = -0.718070331 Simplifying y + -0.125 = -0.718070331 Reorder the terms: -0.125 + y = -0.718070331 Solving -0.125 + y = -0.718070331 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + y = -0.718070331 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + y = -0.718070331 + 0.125 y = -0.718070331 + 0.125 Combine like terms: -0.718070331 + 0.125 = -0.593070331 y = -0.593070331 Simplifying y = -0.593070331Solution
The solution to the problem is based on the solutions from the subproblems. y = {0.843070331, -0.593070331}
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