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Simplifying -4y(7y + 9) = 3(3 + -5y) + -4y Reorder the terms: -4y(9 + 7y) = 3(3 + -5y) + -4y (9 * -4y + 7y * -4y) = 3(3 + -5y) + -4y (-36y + -28y2) = 3(3 + -5y) + -4y -36y + -28y2 = (3 * 3 + -5y * 3) + -4y -36y + -28y2 = (9 + -15y) + -4y Combine like terms: -15y + -4y = -19y -36y + -28y2 = 9 + -19y Solving -36y + -28y2 = 9 + -19y Solving for variable 'y'. Reorder the terms: -9 + -36y + 19y + -28y2 = 9 + -19y + -9 + 19y Combine like terms: -36y + 19y = -17y -9 + -17y + -28y2 = 9 + -19y + -9 + 19y Reorder the terms: -9 + -17y + -28y2 = 9 + -9 + -19y + 19y Combine like terms: 9 + -9 = 0 -9 + -17y + -28y2 = 0 + -19y + 19y -9 + -17y + -28y2 = -19y + 19y Combine like terms: -19y + 19y = 0 -9 + -17y + -28y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 17y + 28y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 17y + 28y2)' equal to zero and attempt to solve: Simplifying 9 + 17y + 28y2 = 0 Solving 9 + 17y + 28y2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. 0.3214285714 + 0.6071428571y + y2 = 0 Move the constant term to the right: Add '-0.3214285714' to each side of the equation. 0.3214285714 + 0.6071428571y + -0.3214285714 + y2 = 0 + -0.3214285714 Reorder the terms: 0.3214285714 + -0.3214285714 + 0.6071428571y + y2 = 0 + -0.3214285714 Combine like terms: 0.3214285714 + -0.3214285714 = 0.0000000000 0.0000000000 + 0.6071428571y + y2 = 0 + -0.3214285714 0.6071428571y + y2 = 0 + -0.3214285714 Combine like terms: 0 + -0.3214285714 = -0.3214285714 0.6071428571y + y2 = -0.3214285714 The y term is 0.6071428571y. Take half its coefficient (0.3035714286). Square it (0.09215561226) and add it to both sides. Add '0.09215561226' to each side of the equation. 0.6071428571y + 0.09215561226 + y2 = -0.3214285714 + 0.09215561226 Reorder the terms: 0.09215561226 + 0.6071428571y + y2 = -0.3214285714 + 0.09215561226 Combine like terms: -0.3214285714 + 0.09215561226 = -0.22927295914 0.09215561226 + 0.6071428571y + y2 = -0.22927295914 Factor a perfect square on the left side: (y + 0.3035714286)(y + 0.3035714286) = -0.22927295914 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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