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Simplifying 3y2 + 15y2 + 2y + 10 = 0 Reorder the terms: 10 + 2y + 3y2 + 15y2 = 0 Combine like terms: 3y2 + 15y2 = 18y2 10 + 2y + 18y2 = 0 Solving 10 + 2y + 18y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + y + 9y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + y + 9y2)' equal to zero and attempt to solve: Simplifying 5 + y + 9y2 = 0 Solving 5 + y + 9y2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + 0.1111111111y + y2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + 0.1111111111y + -0.5555555556 + y2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + 0.1111111111y + y2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + 0.1111111111y + y2 = 0 + -0.5555555556 0.1111111111y + y2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 0.1111111111y + y2 = -0.5555555556 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. 0.1111111111y + 0.25 + y2 = -0.5555555556 + 0.25 Reorder the terms: 0.25 + 0.1111111111y + y2 = -0.5555555556 + 0.25 Combine like terms: -0.5555555556 + 0.25 = -0.3055555556 0.25 + 0.1111111111y + y2 = -0.3055555556 Factor a perfect square on the left side: (y + 0.5)(y + 0.5) = -0.3055555556 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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