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Simplifying (-3y2 + -7y + -9) + -1(4y2 + 6y + 9) = 0 Reorder the terms: (-9 + -7y + -3y2) + -1(4y2 + 6y + 9) = 0 Remove parenthesis around (-9 + -7y + -3y2) -9 + -7y + -3y2 + -1(4y2 + 6y + 9) = 0 Reorder the terms: -9 + -7y + -3y2 + -1(9 + 6y + 4y2) = 0 -9 + -7y + -3y2 + (9 * -1 + 6y * -1 + 4y2 * -1) = 0 -9 + -7y + -3y2 + (-9 + -6y + -4y2) = 0 Reorder the terms: -9 + -9 + -7y + -6y + -3y2 + -4y2 = 0 Combine like terms: -9 + -9 = -18 -18 + -7y + -6y + -3y2 + -4y2 = 0 Combine like terms: -7y + -6y = -13y -18 + -13y + -3y2 + -4y2 = 0 Combine like terms: -3y2 + -4y2 = -7y2 -18 + -13y + -7y2 = 0 Solving -18 + -13y + -7y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(18 + 13y + 7y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(18 + 13y + 7y2)' equal to zero and attempt to solve: Simplifying 18 + 13y + 7y2 = 0 Solving 18 + 13y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 2.571428571 + 1.857142857y + y2 = 0 Move the constant term to the right: Add '-2.571428571' to each side of the equation. 2.571428571 + 1.857142857y + -2.571428571 + y2 = 0 + -2.571428571 Reorder the terms: 2.571428571 + -2.571428571 + 1.857142857y + y2 = 0 + -2.571428571 Combine like terms: 2.571428571 + -2.571428571 = 0.000000000 0.000000000 + 1.857142857y + y2 = 0 + -2.571428571 1.857142857y + y2 = 0 + -2.571428571 Combine like terms: 0 + -2.571428571 = -2.571428571 1.857142857y + y2 = -2.571428571 The y term is 1.857142857y. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857y + 0.8622448978 + y2 = -2.571428571 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857y + y2 = -2.571428571 + 0.8622448978 Combine like terms: -2.571428571 + 0.8622448978 = -1.7091836732 0.8622448978 + 1.857142857y + y2 = -1.7091836732 Factor a perfect square on the left side: (y + 0.9285714285)(y + 0.9285714285) = -1.7091836732 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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