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Simplifying 6(y + -2) + -3 = -6(-3y + 1) * 6y Reorder the terms: 6(-2 + y) + -3 = -6(-3y + 1) * 6y (-2 * 6 + y * 6) + -3 = -6(-3y + 1) * 6y (-12 + 6y) + -3 = -6(-3y + 1) * 6y Reorder the terms: -12 + -3 + 6y = -6(-3y + 1) * 6y Combine like terms: -12 + -3 = -15 -15 + 6y = -6(-3y + 1) * 6y Reorder the terms: -15 + 6y = -6(1 + -3y) * 6y Reorder the terms for easier multiplication: -15 + 6y = -6 * 6y(1 + -3y) Multiply -6 * 6 -15 + 6y = -36y(1 + -3y) -15 + 6y = (1 * -36y + -3y * -36y) -15 + 6y = (-36y + 108y2) Solving -15 + 6y = -36y + 108y2 Solving for variable 'y'. Combine like terms: 6y + 36y = 42y -15 + 42y + -108y2 = -36y + 108y2 + 36y + -108y2 Reorder the terms: -15 + 42y + -108y2 = -36y + 36y + 108y2 + -108y2 Combine like terms: -36y + 36y = 0 -15 + 42y + -108y2 = 0 + 108y2 + -108y2 -15 + 42y + -108y2 = 108y2 + -108y2 Combine like terms: 108y2 + -108y2 = 0 -15 + 42y + -108y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 14y + -36y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 14y + -36y2)' equal to zero and attempt to solve: Simplifying -5 + 14y + -36y2 = 0 Solving -5 + 14y + -36y2 = 0 Begin completing the square. Divide all terms by -36 the coefficient of the squared term: Divide each side by '-36'. 0.1388888889 + -0.3888888889y + y2 = 0 Move the constant term to the right: Add '-0.1388888889' to each side of the equation. 0.1388888889 + -0.3888888889y + -0.1388888889 + y2 = 0 + -0.1388888889 Reorder the terms: 0.1388888889 + -0.1388888889 + -0.3888888889y + y2 = 0 + -0.1388888889 Combine like terms: 0.1388888889 + -0.1388888889 = 0.0000000000 0.0000000000 + -0.3888888889y + y2 = 0 + -0.1388888889 -0.3888888889y + y2 = 0 + -0.1388888889 Combine like terms: 0 + -0.1388888889 = -0.1388888889 -0.3888888889y + y2 = -0.1388888889 The y term is -0.3888888889y. Take half its coefficient (-0.1944444445). Square it (0.03780864200) and add it to both sides. Add '0.03780864200' to each side of the equation. -0.3888888889y + 0.03780864200 + y2 = -0.1388888889 + 0.03780864200 Reorder the terms: 0.03780864200 + -0.3888888889y + y2 = -0.1388888889 + 0.03780864200 Combine like terms: -0.1388888889 + 0.03780864200 = -0.1010802469 0.03780864200 + -0.3888888889y + y2 = -0.1010802469 Factor a perfect square on the left side: (y + -0.1944444445)(y + -0.1944444445) = -0.1010802469 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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