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Simplifying -5y2 + y + -2 + -5y + -3y2 + -2y + -4 = 0 Reorder the terms: -2 + -4 + y + -5y + -2y + -5y2 + -3y2 = 0 Combine like terms: -2 + -4 = -6 -6 + y + -5y + -2y + -5y2 + -3y2 = 0 Combine like terms: y + -5y = -4y -6 + -4y + -2y + -5y2 + -3y2 = 0 Combine like terms: -4y + -2y = -6y -6 + -6y + -5y2 + -3y2 = 0 Combine like terms: -5y2 + -3y2 = -8y2 -6 + -6y + -8y2 = 0 Solving -6 + -6y + -8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-2'. -2(3 + 3y + 4y2) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(3 + 3y + 4y2)' equal to zero and attempt to solve: Simplifying 3 + 3y + 4y2 = 0 Solving 3 + 3y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 0.75y + y2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.75y + -0.75 + y2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.75y + y2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.75y + y2 = 0 + -0.75 0.75y + y2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.75y + y2 = -0.75 The y term is 0.75y. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75y + 0.140625 + y2 = -0.75 + 0.140625 Reorder the terms: 0.140625 + 0.75y + y2 = -0.75 + 0.140625 Combine like terms: -0.75 + 0.140625 = -0.609375 0.140625 + 0.75y + y2 = -0.609375 Factor a perfect square on the left side: (y + 0.375)(y + 0.375) = -0.609375 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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