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Simplifying (4y2 + 2y + -8) + -1(7y2 + 4 + -1y) = 0 Reorder the terms: (-8 + 2y + 4y2) + -1(7y2 + 4 + -1y) = 0 Remove parenthesis around (-8 + 2y + 4y2) -8 + 2y + 4y2 + -1(7y2 + 4 + -1y) = 0 Reorder the terms: -8 + 2y + 4y2 + -1(4 + -1y + 7y2) = 0 -8 + 2y + 4y2 + (4 * -1 + -1y * -1 + 7y2 * -1) = 0 -8 + 2y + 4y2 + (-4 + 1y + -7y2) = 0 Reorder the terms: -8 + -4 + 2y + 1y + 4y2 + -7y2 = 0 Combine like terms: -8 + -4 = -12 -12 + 2y + 1y + 4y2 + -7y2 = 0 Combine like terms: 2y + 1y = 3y -12 + 3y + 4y2 + -7y2 = 0 Combine like terms: 4y2 + -7y2 = -3y2 -12 + 3y + -3y2 = 0 Solving -12 + 3y + -3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + y + -1y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + y + -1y2)' equal to zero and attempt to solve: Simplifying -4 + y + -1y2 = 0 Solving -4 + y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -1y + y2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1y + -4 + y2 = 0 + -4 Reorder the terms: 4 + -4 + -1y + y2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1y + y2 = 0 + -4 -1y + y2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1y + y2 = -4 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. -1y + 0.25 + y2 = -4 + 0.25 Reorder the terms: 0.25 + -1y + y2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -1y + y2 = -3.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -3.75 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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