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Simplifying 2y + -3 = 3y2 + -10y + 12 Reorder the terms: -3 + 2y = 3y2 + -10y + 12 Reorder the terms: -3 + 2y = 12 + -10y + 3y2 Solving -3 + 2y = 12 + -10y + 3y2 Solving for variable 'y'. Reorder the terms: -3 + -12 + 2y + 10y + -3y2 = 12 + -10y + 3y2 + -12 + 10y + -3y2 Combine like terms: -3 + -12 = -15 -15 + 2y + 10y + -3y2 = 12 + -10y + 3y2 + -12 + 10y + -3y2 Combine like terms: 2y + 10y = 12y -15 + 12y + -3y2 = 12 + -10y + 3y2 + -12 + 10y + -3y2 Reorder the terms: -15 + 12y + -3y2 = 12 + -12 + -10y + 10y + 3y2 + -3y2 Combine like terms: 12 + -12 = 0 -15 + 12y + -3y2 = 0 + -10y + 10y + 3y2 + -3y2 -15 + 12y + -3y2 = -10y + 10y + 3y2 + -3y2 Combine like terms: -10y + 10y = 0 -15 + 12y + -3y2 = 0 + 3y2 + -3y2 -15 + 12y + -3y2 = 3y2 + -3y2 Combine like terms: 3y2 + -3y2 = 0 -15 + 12y + -3y2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 4y + -1y2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 4y + -1y2)' equal to zero and attempt to solve: Simplifying -5 + 4y + -1y2 = 0 Solving -5 + 4y + -1y2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -4y + y2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -4y + -5 + y2 = 0 + -5 Reorder the terms: 5 + -5 + -4y + y2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4y + y2 = 0 + -5 -4y + y2 = 0 + -5 Combine like terms: 0 + -5 = -5 -4y + y2 = -5 The y term is -4y. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4y + 4 + y2 = -5 + 4 Reorder the terms: 4 + -4y + y2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + -4y + y2 = -1 Factor a perfect square on the left side: (y + -2)(y + -2) = -1 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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