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Simplifying (8y2 + -3y + -10) + (-11y2 + 2y + -7) = 0 Reorder the terms: (-10 + -3y + 8y2) + (-11y2 + 2y + -7) = 0 Remove parenthesis around (-10 + -3y + 8y2) -10 + -3y + 8y2 + (-11y2 + 2y + -7) = 0 Reorder the terms: -10 + -3y + 8y2 + (-7 + 2y + -11y2) = 0 Remove parenthesis around (-7 + 2y + -11y2) -10 + -3y + 8y2 + -7 + 2y + -11y2 = 0 Reorder the terms: -10 + -7 + -3y + 2y + 8y2 + -11y2 = 0 Combine like terms: -10 + -7 = -17 -17 + -3y + 2y + 8y2 + -11y2 = 0 Combine like terms: -3y + 2y = -1y -17 + -1y + 8y2 + -11y2 = 0 Combine like terms: 8y2 + -11y2 = -3y2 -17 + -1y + -3y2 = 0 Solving -17 + -1y + -3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(17 + y + 3y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(17 + y + 3y2)' equal to zero and attempt to solve: Simplifying 17 + y + 3y2 = 0 Solving 17 + y + 3y2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 5.666666667 + 0.3333333333y + y2 = 0 Move the constant term to the right: Add '-5.666666667' to each side of the equation. 5.666666667 + 0.3333333333y + -5.666666667 + y2 = 0 + -5.666666667 Reorder the terms: 5.666666667 + -5.666666667 + 0.3333333333y + y2 = 0 + -5.666666667 Combine like terms: 5.666666667 + -5.666666667 = 0.000000000 0.000000000 + 0.3333333333y + y2 = 0 + -5.666666667 0.3333333333y + y2 = 0 + -5.666666667 Combine like terms: 0 + -5.666666667 = -5.666666667 0.3333333333y + y2 = -5.666666667 The y term is y. 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. 0.3333333333y + 0.25 + y2 = -5.666666667 + 0.25 Reorder the terms: 0.25 + 0.3333333333y + y2 = -5.666666667 + 0.25 Combine like terms: -5.666666667 + 0.25 = -5.416666667 0.25 + 0.3333333333y + y2 = -5.416666667 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -5.416666667 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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