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Simplifying -4y2 + -12y + -23 = 0 Reorder the terms: -23 + -12y + -4y2 = 0 Solving -23 + -12y + -4y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(23 + 12y + 4y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(23 + 12y + 4y2)' equal to zero and attempt to solve: Simplifying 23 + 12y + 4y2 = 0 Solving 23 + 12y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.75 + 3y + y2 = 0 Move the constant term to the right: Add '-5.75' to each side of the equation. 5.75 + 3y + -5.75 + y2 = 0 + -5.75 Reorder the terms: 5.75 + -5.75 + 3y + y2 = 0 + -5.75 Combine like terms: 5.75 + -5.75 = 0.00 0.00 + 3y + y2 = 0 + -5.75 3y + y2 = 0 + -5.75 Combine like terms: 0 + -5.75 = -5.75 3y + y2 = -5.75 The y term is 3y. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3y + 2.25 + y2 = -5.75 + 2.25 Reorder the terms: 2.25 + 3y + y2 = -5.75 + 2.25 Combine like terms: -5.75 + 2.25 = -3.5 2.25 + 3y + y2 = -3.5 Factor a perfect square on the left side: (y + 1.5)(y + 1.5) = -3.5 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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