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Simplifying 4y + 6y2 + 5 + 2y2 + 3 = 0 Reorder the terms: 5 + 3 + 4y + 6y2 + 2y2 = 0 Combine like terms: 5 + 3 = 8 8 + 4y + 6y2 + 2y2 = 0 Combine like terms: 6y2 + 2y2 = 8y2 8 + 4y + 8y2 = 0 Solving 8 + 4y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(2 + y + 2y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(2 + y + 2y2)' equal to zero and attempt to solve: Simplifying 2 + y + 2y2 = 0 Solving 2 + y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 0.5y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 0.5y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + 0.5y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 0.5y + y2 = 0 + -1 0.5y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 0.5y + y2 = -1 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. 0.5y + 0.25 + y2 = -1 + 0.25 Reorder the terms: 0.25 + 0.5y + y2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + 0.5y + y2 = -0.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -0.75 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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