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Simplifying 3y2 + -4y + 9 + 7y2 + -6y + -1 + 4y2 + 4y + 2 = 0 Reorder the terms: 9 + -1 + 2 + -4y + -6y + 4y + 3y2 + 7y2 + 4y2 = 0 Combine like terms: 9 + -1 = 8 8 + 2 + -4y + -6y + 4y + 3y2 + 7y2 + 4y2 = 0 Combine like terms: 8 + 2 = 10 10 + -4y + -6y + 4y + 3y2 + 7y2 + 4y2 = 0 Combine like terms: -4y + -6y = -10y 10 + -10y + 4y + 3y2 + 7y2 + 4y2 = 0 Combine like terms: -10y + 4y = -6y 10 + -6y + 3y2 + 7y2 + 4y2 = 0 Combine like terms: 3y2 + 7y2 = 10y2 10 + -6y + 10y2 + 4y2 = 0 Combine like terms: 10y2 + 4y2 = 14y2 10 + -6y + 14y2 = 0 Solving 10 + -6y + 14y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -3y + 7y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -3y + 7y2)' equal to zero and attempt to solve: Simplifying 5 + -3y + 7y2 = 0 Solving 5 + -3y + 7y2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.7142857143 + -0.4285714286y + y2 = 0 Move the constant term to the right: Add '-0.7142857143' to each side of the equation. 0.7142857143 + -0.4285714286y + -0.7142857143 + y2 = 0 + -0.7142857143 Reorder the terms: 0.7142857143 + -0.7142857143 + -0.4285714286y + y2 = 0 + -0.7142857143 Combine like terms: 0.7142857143 + -0.7142857143 = 0.0000000000 0.0000000000 + -0.4285714286y + y2 = 0 + -0.7142857143 -0.4285714286y + y2 = 0 + -0.7142857143 Combine like terms: 0 + -0.7142857143 = -0.7142857143 -0.4285714286y + y2 = -0.7142857143 The y term is -0.4285714286y. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286y + 0.04591836735 + y2 = -0.7142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286y + y2 = -0.7142857143 + 0.04591836735 Combine like terms: -0.7142857143 + 0.04591836735 = -0.66836734695 0.04591836735 + -0.4285714286y + y2 = -0.66836734695 Factor a perfect square on the left side: (y + -0.2142857143)(y + -0.2142857143) = -0.66836734695 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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