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Simplifying -2(5y + -1) * y = -4(y + -3) Reorder the terms: -2(-1 + 5y) * y = -4(y + -3) Reorder the terms for easier multiplication: -2y(-1 + 5y) = -4(y + -3) (-1 * -2y + 5y * -2y) = -4(y + -3) (2y + -10y2) = -4(y + -3) Reorder the terms: 2y + -10y2 = -4(-3 + y) 2y + -10y2 = (-3 * -4 + y * -4) 2y + -10y2 = (12 + -4y) Solving 2y + -10y2 = 12 + -4y Solving for variable 'y'. Reorder the terms: -12 + 2y + 4y + -10y2 = 12 + -4y + -12 + 4y Combine like terms: 2y + 4y = 6y -12 + 6y + -10y2 = 12 + -4y + -12 + 4y Reorder the terms: -12 + 6y + -10y2 = 12 + -12 + -4y + 4y Combine like terms: 12 + -12 = 0 -12 + 6y + -10y2 = 0 + -4y + 4y -12 + 6y + -10y2 = -4y + 4y Combine like terms: -4y + 4y = 0 -12 + 6y + -10y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-6 + 3y + -5y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + 3y + -5y2)' equal to zero and attempt to solve: Simplifying -6 + 3y + -5y2 = 0 Solving -6 + 3y + -5y2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 1.2 + -0.6y + y2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + -0.6y + -1.2 + y2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + -0.6y + y2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + -0.6y + y2 = 0 + -1.2 -0.6y + y2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 -0.6y + y2 = -1.2 The y term is -0.6y. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6y + 0.09 + y2 = -1.2 + 0.09 Reorder the terms: 0.09 + -0.6y + y2 = -1.2 + 0.09 Combine like terms: -1.2 + 0.09 = -1.11 0.09 + -0.6y + y2 = -1.11 Factor a perfect square on the left side: (y + -0.3)(y + -0.3) = -1.11 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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