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Simplifying (5y2 + -1y + 3) + -1(-5 + 5y + -3y2) = 0 Reorder the terms: (3 + -1y + 5y2) + -1(-5 + 5y + -3y2) = 0 Remove parenthesis around (3 + -1y + 5y2) 3 + -1y + 5y2 + -1(-5 + 5y + -3y2) = 0 3 + -1y + 5y2 + (-5 * -1 + 5y * -1 + -3y2 * -1) = 0 3 + -1y + 5y2 + (5 + -5y + 3y2) = 0 Reorder the terms: 3 + 5 + -1y + -5y + 5y2 + 3y2 = 0 Combine like terms: 3 + 5 = 8 8 + -1y + -5y + 5y2 + 3y2 = 0 Combine like terms: -1y + -5y = -6y 8 + -6y + 5y2 + 3y2 = 0 Combine like terms: 5y2 + 3y2 = 8y2 8 + -6y + 8y2 = 0 Solving 8 + -6y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(4 + -3y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3y + 4y2)' equal to zero and attempt to solve: Simplifying 4 + -3y + 4y2 = 0 Solving 4 + -3y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1 + -0.75y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -0.75y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -0.75y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.75y + y2 = 0 + -1 -0.75y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.75y + y2 = -1 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 = -1 + 0.140625 Reorder the terms: 0.140625 + -0.75y + y2 = -1 + 0.140625 Combine like terms: -1 + 0.140625 = -0.859375 0.140625 + -0.75y + y2 = -0.859375 Factor a perfect square on the left side: (y + -0.375)(y + -0.375) = -0.859375 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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