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Simplifying 9(4y2 + 2y + 3) = 0 Reorder the terms: 9(3 + 2y + 4y2) = 0 (3 * 9 + 2y * 9 + 4y2 * 9) = 0 (27 + 18y + 36y2) = 0 Solving 27 + 18y + 36y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '9'. 9(3 + 2y + 4y2) = 0 Ignore the factor 9.Subproblem 1
Set the factor '(3 + 2y + 4y2)' equal to zero and attempt to solve: Simplifying 3 + 2y + 4y2 = 0 Solving 3 + 2y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.75 + 0.5y + y2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + 0.5y + -0.75 + y2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + 0.5y + y2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + 0.5y + y2 = 0 + -0.75 0.5y + y2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 0.5y + y2 = -0.75 The y term is 0.5y. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5y + 0.0625 + y2 = -0.75 + 0.0625 Reorder the terms: 0.0625 + 0.5y + y2 = -0.75 + 0.0625 Combine like terms: -0.75 + 0.0625 = -0.6875 0.0625 + 0.5y + y2 = -0.6875 Factor a perfect square on the left side: (y + 0.25)(y + 0.25) = -0.6875 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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