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Simplifying (9y2 + -5y + 6) + -1(3y2 + y + -4) = 0 Reorder the terms: (6 + -5y + 9y2) + -1(3y2 + y + -4) = 0 Remove parenthesis around (6 + -5y + 9y2) 6 + -5y + 9y2 + -1(3y2 + y + -4) = 0 Reorder the terms: 6 + -5y + 9y2 + -1(-4 + y + 3y2) = 0 6 + -5y + 9y2 + (-4 * -1 + y * -1 + 3y2 * -1) = 0 6 + -5y + 9y2 + (4 + -1y + -3y2) = 0 Reorder the terms: 6 + 4 + -5y + -1y + 9y2 + -3y2 = 0 Combine like terms: 6 + 4 = 10 10 + -5y + -1y + 9y2 + -3y2 = 0 Combine like terms: -5y + -1y = -6y 10 + -6y + 9y2 + -3y2 = 0 Combine like terms: 9y2 + -3y2 = 6y2 10 + -6y + 6y2 = 0 Solving 10 + -6y + 6y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -3y + 3y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -3y + 3y2)' equal to zero and attempt to solve: Simplifying 5 + -3y + 3y2 = 0 Solving 5 + -3y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + -1y + y2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + -1y + -1.666666667 + y2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + -1y + y2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + -1y + y2 = 0 + -1.666666667 -1y + y2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 -1y + y2 = -1.666666667 The y term is -1y. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1y + 0.25 + y2 = -1.666666667 + 0.25 Reorder the terms: 0.25 + -1y + y2 = -1.666666667 + 0.25 Combine like terms: -1.666666667 + 0.25 = -1.416666667 0.25 + -1y + y2 = -1.416666667 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = -1.416666667 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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