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Simplifying 5y3(5y2 + -7y + 9) = 0 Reorder the terms: 5y3(9 + -7y + 5y2) = 0 (9 * 5y3 + -7y * 5y3 + 5y2 * 5y3) = 0 (45y3 + -35y4 + 25y5) = 0 Solving 45y3 + -35y4 + 25y5 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '5y3'. 5y3(9 + -7y + 5y2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'y3' equal to zero and attempt to solve: Simplifying y3 = 0 Solving y3 = 0 Move all terms containing y to the left, all other terms to the right. Simplifying y3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(9 + -7y + 5y2)' equal to zero and attempt to solve: Simplifying 9 + -7y + 5y2 = 0 Solving 9 + -7y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.8 + -1.4y + y2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -1.4y + -1.8 + y2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -1.4y + y2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -1.4y + y2 = 0 + -1.8 -1.4y + y2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -1.4y + y2 = -1.8 The y term is -1.4y. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4y + 0.49 + y2 = -1.8 + 0.49 Reorder the terms: 0.49 + -1.4y + y2 = -1.8 + 0.49 Combine like terms: -1.8 + 0.49 = -1.31 0.49 + -1.4y + y2 = -1.31 Factor a perfect square on the left side: (y + -0.7)(y + -0.7) = -1.31 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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