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Simplifying -4y + 4 = -4y(2y + 3) Reorder the terms: 4 + -4y = -4y(2y + 3) Reorder the terms: 4 + -4y = -4y(3 + 2y) 4 + -4y = (3 * -4y + 2y * -4y) 4 + -4y = (-12y + -8y2) Solving 4 + -4y = -12y + -8y2 Solving for variable 'y'. Combine like terms: -4y + 12y = 8y 4 + 8y + 8y2 = -12y + -8y2 + 12y + 8y2 Reorder the terms: 4 + 8y + 8y2 = -12y + 12y + -8y2 + 8y2 Combine like terms: -12y + 12y = 0 4 + 8y + 8y2 = 0 + -8y2 + 8y2 4 + 8y + 8y2 = -8y2 + 8y2 Combine like terms: -8y2 + 8y2 = 0 4 + 8y + 8y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 2y + 2y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 2y + 2y2)' equal to zero and attempt to solve: Simplifying 1 + 2y + 2y2 = 0 Solving 1 + 2y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + y + y2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + y + -0.5 + y2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + y + y2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + y + y2 = 0 + -0.5 y + y2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 y + y2 = -0.5 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. + 0.25 + y2 = -0.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 1.25 + y2 = -0.25 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -0.25 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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