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Simplifying (-8y2 + -7y + -2) + -1(5y2 + 6y + 4) = 0 Reorder the terms: (-2 + -7y + -8y2) + -1(5y2 + 6y + 4) = 0 Remove parenthesis around (-2 + -7y + -8y2) -2 + -7y + -8y2 + -1(5y2 + 6y + 4) = 0 Reorder the terms: -2 + -7y + -8y2 + -1(4 + 6y + 5y2) = 0 -2 + -7y + -8y2 + (4 * -1 + 6y * -1 + 5y2 * -1) = 0 -2 + -7y + -8y2 + (-4 + -6y + -5y2) = 0 Reorder the terms: -2 + -4 + -7y + -6y + -8y2 + -5y2 = 0 Combine like terms: -2 + -4 = -6 -6 + -7y + -6y + -8y2 + -5y2 = 0 Combine like terms: -7y + -6y = -13y -6 + -13y + -8y2 + -5y2 = 0 Combine like terms: -8y2 + -5y2 = -13y2 -6 + -13y + -13y2 = 0 Solving -6 + -13y + -13y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 13y + 13y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 13y + 13y2)' equal to zero and attempt to solve: Simplifying 6 + 13y + 13y2 = 0 Solving 6 + 13y + 13y2 = 0 Begin completing the square. Divide all terms by 13 the coefficient of the squared term: Divide each side by '13'. 0.4615384615 + y + y2 = 0 Move the constant term to the right: Add '-0.4615384615' to each side of the equation. 0.4615384615 + y + -0.4615384615 + y2 = 0 + -0.4615384615 Reorder the terms: 0.4615384615 + -0.4615384615 + y + y2 = 0 + -0.4615384615 Combine like terms: 0.4615384615 + -0.4615384615 = 0.0000000000 0.0000000000 + y + y2 = 0 + -0.4615384615 y + y2 = 0 + -0.4615384615 Combine like terms: 0 + -0.4615384615 = -0.4615384615 y + y2 = -0.4615384615 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. + 0.25 + y2 = -0.4615384615 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + y2 = -0.4615384615 + 0.25 Combine like terms: -0.4615384615 + 0.25 = -0.2115384615 1.25 + y2 = -0.2115384615 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -0.2115384615 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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