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Simplifying (4y2 + -3y + -7) + -1(6y2 + y + 2) = 0 Reorder the terms: (-7 + -3y + 4y2) + -1(6y2 + y + 2) = 0 Remove parenthesis around (-7 + -3y + 4y2) -7 + -3y + 4y2 + -1(6y2 + y + 2) = 0 Reorder the terms: -7 + -3y + 4y2 + -1(2 + y + 6y2) = 0 -7 + -3y + 4y2 + (2 * -1 + y * -1 + 6y2 * -1) = 0 -7 + -3y + 4y2 + (-2 + -1y + -6y2) = 0 Reorder the terms: -7 + -2 + -3y + -1y + 4y2 + -6y2 = 0 Combine like terms: -7 + -2 = -9 -9 + -3y + -1y + 4y2 + -6y2 = 0 Combine like terms: -3y + -1y = -4y -9 + -4y + 4y2 + -6y2 = 0 Combine like terms: 4y2 + -6y2 = -2y2 -9 + -4y + -2y2 = 0 Solving -9 + -4y + -2y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 4y + 2y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 4y + 2y2)' equal to zero and attempt to solve: Simplifying 9 + 4y + 2y2 = 0 Solving 9 + 4y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 4.5 + 2y + y2 = 0 Move the constant term to the right: Add '-4.5' to each side of the equation. 4.5 + 2y + -4.5 + y2 = 0 + -4.5 Reorder the terms: 4.5 + -4.5 + 2y + y2 = 0 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + 2y + y2 = 0 + -4.5 2y + y2 = 0 + -4.5 Combine like terms: 0 + -4.5 = -4.5 2y + y2 = -4.5 The y term is 2y. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2y + 1 + y2 = -4.5 + 1 Reorder the terms: 1 + 2y + y2 = -4.5 + 1 Combine like terms: -4.5 + 1 = -3.5 1 + 2y + y2 = -3.5 Factor a perfect square on the left side: (y + 1)(y + 1) = -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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