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Simplifying (-9y2 + 6y + -1) + -1(5y2 + 7y + 4) = 0 Reorder the terms: (-1 + 6y + -9y2) + -1(5y2 + 7y + 4) = 0 Remove parenthesis around (-1 + 6y + -9y2) -1 + 6y + -9y2 + -1(5y2 + 7y + 4) = 0 Reorder the terms: -1 + 6y + -9y2 + -1(4 + 7y + 5y2) = 0 -1 + 6y + -9y2 + (4 * -1 + 7y * -1 + 5y2 * -1) = 0 -1 + 6y + -9y2 + (-4 + -7y + -5y2) = 0 Reorder the terms: -1 + -4 + 6y + -7y + -9y2 + -5y2 = 0 Combine like terms: -1 + -4 = -5 -5 + 6y + -7y + -9y2 + -5y2 = 0 Combine like terms: 6y + -7y = -1y -5 + -1y + -9y2 + -5y2 = 0 Combine like terms: -9y2 + -5y2 = -14y2 -5 + -1y + -14y2 = 0 Solving -5 + -1y + -14y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + y + 14y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + y + 14y2)' equal to zero and attempt to solve: Simplifying 5 + y + 14y2 = 0 Solving 5 + y + 14y2 = 0 Begin completing the square. Divide all terms by 14 the coefficient of the squared term: Divide each side by '14'. 0.3571428571 + 0.07142857143y + y2 = 0 Move the constant term to the right: Add '-0.3571428571' to each side of the equation. 0.3571428571 + 0.07142857143y + -0.3571428571 + y2 = 0 + -0.3571428571 Reorder the terms: 0.3571428571 + -0.3571428571 + 0.07142857143y + y2 = 0 + -0.3571428571 Combine like terms: 0.3571428571 + -0.3571428571 = 0.0000000000 0.0000000000 + 0.07142857143y + y2 = 0 + -0.3571428571 0.07142857143y + y2 = 0 + -0.3571428571 Combine like terms: 0 + -0.3571428571 = -0.3571428571 0.07142857143y + y2 = -0.3571428571 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. 0.07142857143y + 0.25 + y2 = -0.3571428571 + 0.25 Reorder the terms: 0.25 + 0.07142857143y + y2 = -0.3571428571 + 0.25 Combine like terms: -0.3571428571 + 0.25 = -0.1071428571 0.25 + 0.07142857143y + y2 = -0.1071428571 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -0.1071428571 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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