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Simplifying 7y + -2y(y + 4) = 24 Reorder the terms: 7y + -2y(4 + y) = 24 7y + (4 * -2y + y * -2y) = 24 7y + (-8y + -2y2) = 24 Combine like terms: 7y + -8y = -1y -1y + -2y2 = 24 Solving -1y + -2y2 = 24 Solving for variable 'y'. Reorder the terms: -24 + -1y + -2y2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + -1y + -2y2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(24 + y + 2y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(24 + y + 2y2)' equal to zero and attempt to solve: Simplifying 24 + y + 2y2 = 0 Solving 24 + y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12 + 0.5y + y2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + 0.5y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + 0.5y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + 0.5y + y2 = 0 + -12 0.5y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 0.5y + y2 = -12 The y term is y. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5y + 0.25 + y2 = -12 + 0.25 Reorder the terms: 0.25 + 0.5y + y2 = -12 + 0.25 Combine like terms: -12 + 0.25 = -11.75 0.25 + 0.5y + y2 = -11.75 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -11.75 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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