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Simplifying 0 = 8y2 + -12y + 8 Reorder the terms: 0 = 8 + -12y + 8y2 Solving 0 = 8 + -12y + 8y2 Solving for variable 'y'. Combine like terms: 0 + -8 = -8 -8 + 12y + -8y2 = 8 + -12y + 8y2 + -8 + 12y + -8y2 Reorder the terms: -8 + 12y + -8y2 = 8 + -8 + -12y + 12y + 8y2 + -8y2 Combine like terms: 8 + -8 = 0 -8 + 12y + -8y2 = 0 + -12y + 12y + 8y2 + -8y2 -8 + 12y + -8y2 = -12y + 12y + 8y2 + -8y2 Combine like terms: -12y + 12y = 0 -8 + 12y + -8y2 = 0 + 8y2 + -8y2 -8 + 12y + -8y2 = 8y2 + -8y2 Combine like terms: 8y2 + -8y2 = 0 -8 + 12y + -8y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2 + 3y + -2y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + 3y + -2y2)' equal to zero and attempt to solve: Simplifying -2 + 3y + -2y2 = 0 Solving -2 + 3y + -2y2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1 + -1.5y + y2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.5y + -1 + y2 = 0 + -1 Reorder the terms: 1 + -1 + -1.5y + y2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.5y + y2 = 0 + -1 -1.5y + y2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.5y + y2 = -1 The y term is -1.5y. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5y + 0.5625 + y2 = -1 + 0.5625 Reorder the terms: 0.5625 + -1.5y + y2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + -1.5y + y2 = -0.4375 Factor a perfect square on the left side: (y + -0.75)(y + -0.75) = -0.4375 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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