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Simplifying (-9y2 + -5y + -3) + -1(3y2 + 8y + 3) = 0 Reorder the terms: (-3 + -5y + -9y2) + -1(3y2 + 8y + 3) = 0 Remove parenthesis around (-3 + -5y + -9y2) -3 + -5y + -9y2 + -1(3y2 + 8y + 3) = 0 Reorder the terms: -3 + -5y + -9y2 + -1(3 + 8y + 3y2) = 0 -3 + -5y + -9y2 + (3 * -1 + 8y * -1 + 3y2 * -1) = 0 -3 + -5y + -9y2 + (-3 + -8y + -3y2) = 0 Reorder the terms: -3 + -3 + -5y + -8y + -9y2 + -3y2 = 0 Combine like terms: -3 + -3 = -6 -6 + -5y + -8y + -9y2 + -3y2 = 0 Combine like terms: -5y + -8y = -13y -6 + -13y + -9y2 + -3y2 = 0 Combine like terms: -9y2 + -3y2 = -12y2 -6 + -13y + -12y2 = 0 Solving -6 + -13y + -12y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 13y + 12y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 13y + 12y2)' equal to zero and attempt to solve: Simplifying 6 + 13y + 12y2 = 0 Solving 6 + 13y + 12y2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5 + 1.083333333y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 1.083333333y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 1.083333333y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 1.083333333y + y2 = 0 + -0.5 1.083333333y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 1.083333333y + y2 = -0.5 The y term is 1.083333333y. Take half its coefficient (0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. 1.083333333y + 0.2934027776 + y2 = -0.5 + 0.2934027776 Reorder the terms: 0.2934027776 + 1.083333333y + y2 = -0.5 + 0.2934027776 Combine like terms: -0.5 + 0.2934027776 = -0.2065972224 0.2934027776 + 1.083333333y + y2 = -0.2065972224 Factor a perfect square on the left side: (y + 0.5416666665)(y + 0.5416666665) = -0.2065972224 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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