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Simplifying 8y2 + 28y + 42 = 0 Reorder the terms: 42 + 28y + 8y2 = 0 Solving 42 + 28y + 8y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(21 + 14y + 4y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(21 + 14y + 4y2)' equal to zero and attempt to solve: Simplifying 21 + 14y + 4y2 = 0 Solving 21 + 14y + 4y2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 5.25 + 3.5y + y2 = 0 Move the constant term to the right: Add '-5.25' to each side of the equation. 5.25 + 3.5y + -5.25 + y2 = 0 + -5.25 Reorder the terms: 5.25 + -5.25 + 3.5y + y2 = 0 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + 3.5y + y2 = 0 + -5.25 3.5y + y2 = 0 + -5.25 Combine like terms: 0 + -5.25 = -5.25 3.5y + y2 = -5.25 The y term is 3.5y. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5y + 3.0625 + y2 = -5.25 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = -5.25 + 3.0625 Combine like terms: -5.25 + 3.0625 = -2.1875 3.0625 + 3.5y + y2 = -2.1875 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = -2.1875 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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