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Simplifying 2y + 4y(y + 3) = -30 Reorder the terms: 2y + 4y(3 + y) = -30 2y + (3 * 4y + y * 4y) = -30 2y + (12y + 4y2) = -30 Combine like terms: 2y + 12y = 14y 14y + 4y2 = -30 Solving 14y + 4y2 = -30 Solving for variable 'y'. Reorder the terms: 30 + 14y + 4y2 = -30 + 30 Combine like terms: -30 + 30 = 0 30 + 14y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(15 + 7y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(15 + 7y + 2y2)' equal to zero and attempt to solve: Simplifying 15 + 7y + 2y2 = 0 Solving 15 + 7y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 3.5y + y2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 3.5y + -7.5 + y2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 3.5y + y2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 3.5y + y2 = 0 + -7.5 3.5y + y2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 3.5y + y2 = -7.5 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 = -7.5 + 3.0625 Reorder the terms: 3.0625 + 3.5y + y2 = -7.5 + 3.0625 Combine like terms: -7.5 + 3.0625 = -4.4375 3.0625 + 3.5y + y2 = -4.4375 Factor a perfect square on the left side: (y + 1.75)(y + 1.75) = -4.4375 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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