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Simplifying (-6y2 + -8y + -1) + -1(5y2 + 5y + 3) = 0 Reorder the terms: (-1 + -8y + -6y2) + -1(5y2 + 5y + 3) = 0 Remove parenthesis around (-1 + -8y + -6y2) -1 + -8y + -6y2 + -1(5y2 + 5y + 3) = 0 Reorder the terms: -1 + -8y + -6y2 + -1(3 + 5y + 5y2) = 0 -1 + -8y + -6y2 + (3 * -1 + 5y * -1 + 5y2 * -1) = 0 -1 + -8y + -6y2 + (-3 + -5y + -5y2) = 0 Reorder the terms: -1 + -3 + -8y + -5y + -6y2 + -5y2 = 0 Combine like terms: -1 + -3 = -4 -4 + -8y + -5y + -6y2 + -5y2 = 0 Combine like terms: -8y + -5y = -13y -4 + -13y + -6y2 + -5y2 = 0 Combine like terms: -6y2 + -5y2 = -11y2 -4 + -13y + -11y2 = 0 Solving -4 + -13y + -11y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 13y + 11y2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 13y + 11y2)' equal to zero and attempt to solve: Simplifying 4 + 13y + 11y2 = 0 Solving 4 + 13y + 11y2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.3636363636 + 1.181818182y + y2 = 0 Move the constant term to the right: Add '-0.3636363636' to each side of the equation. 0.3636363636 + 1.181818182y + -0.3636363636 + y2 = 0 + -0.3636363636 Reorder the terms: 0.3636363636 + -0.3636363636 + 1.181818182y + y2 = 0 + -0.3636363636 Combine like terms: 0.3636363636 + -0.3636363636 = 0.0000000000 0.0000000000 + 1.181818182y + y2 = 0 + -0.3636363636 1.181818182y + y2 = 0 + -0.3636363636 Combine like terms: 0 + -0.3636363636 = -0.3636363636 1.181818182y + y2 = -0.3636363636 The y term is 1.181818182y. Take half its coefficient (0.590909091). Square it (0.3491735538) and add it to both sides. Add '0.3491735538' to each side of the equation. 1.181818182y + 0.3491735538 + y2 = -0.3636363636 + 0.3491735538 Reorder the terms: 0.3491735538 + 1.181818182y + y2 = -0.3636363636 + 0.3491735538 Combine like terms: -0.3636363636 + 0.3491735538 = -0.0144628098 0.3491735538 + 1.181818182y + y2 = -0.0144628098 Factor a perfect square on the left side: (y + 0.590909091)(y + 0.590909091) = -0.0144628098 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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