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Simplifying 6(5y2 + -8y + 7) + -2(8y2 + -6y + 9) = 0 Reorder the terms: 6(7 + -8y + 5y2) + -2(8y2 + -6y + 9) = 0 (7 * 6 + -8y * 6 + 5y2 * 6) + -2(8y2 + -6y + 9) = 0 (42 + -48y + 30y2) + -2(8y2 + -6y + 9) = 0 Reorder the terms: 42 + -48y + 30y2 + -2(9 + -6y + 8y2) = 0 42 + -48y + 30y2 + (9 * -2 + -6y * -2 + 8y2 * -2) = 0 42 + -48y + 30y2 + (-18 + 12y + -16y2) = 0 Reorder the terms: 42 + -18 + -48y + 12y + 30y2 + -16y2 = 0 Combine like terms: 42 + -18 = 24 24 + -48y + 12y + 30y2 + -16y2 = 0 Combine like terms: -48y + 12y = -36y 24 + -36y + 30y2 + -16y2 = 0 Combine like terms: 30y2 + -16y2 = 14y2 24 + -36y + 14y2 = 0 Solving 24 + -36y + 14y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -18y + 7y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(12 + -18y + 7y2)' equal to zero and attempt to solve: Simplifying 12 + -18y + 7y2 = 0 Solving 12 + -18y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.714285714 + -2.571428571y + y2 = 0 Move the constant term to the right: Add '-1.714285714' to each side of the equation. 1.714285714 + -2.571428571y + -1.714285714 + y2 = 0 + -1.714285714 Reorder the terms: 1.714285714 + -1.714285714 + -2.571428571y + y2 = 0 + -1.714285714 Combine like terms: 1.714285714 + -1.714285714 = 0.000000000 0.000000000 + -2.571428571y + y2 = 0 + -1.714285714 -2.571428571y + y2 = 0 + -1.714285714 Combine like terms: 0 + -1.714285714 = -1.714285714 -2.571428571y + y2 = -1.714285714 The y term is -2.571428571y. Take half its coefficient (-1.285714286). Square it (1.653061225) and add it to both sides. Add '1.653061225' to each side of the equation. -2.571428571y + 1.653061225 + y2 = -1.714285714 + 1.653061225 Reorder the terms: 1.653061225 + -2.571428571y + y2 = -1.714285714 + 1.653061225 Combine like terms: -1.714285714 + 1.653061225 = -0.061224489 1.653061225 + -2.571428571y + y2 = -0.061224489 Factor a perfect square on the left side: (y + -1.285714286)(y + -1.285714286) = -0.061224489 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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