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