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Simplifying 10y2 + -5y + 4 = 3y Reorder the terms: 4 + -5y + 10y2 = 3y Solving 4 + -5y + 10y2 = 3y Solving for variable 'y'. Reorder the terms: 4 + -5y + -3y + 10y2 = 3y + -3y Combine like terms: -5y + -3y = -8y 4 + -8y + 10y2 = 3y + -3y Combine like terms: 3y + -3y = 0 4 + -8y + 10y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(2 + -4y + 5y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -4y + 5y2)' equal to zero and attempt to solve: Simplifying 2 + -4y + 5y2 = 0 Solving 2 + -4y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + -0.8y + y2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + -0.8y + -0.4 + y2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + -0.8y + y2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + -0.8y + y2 = 0 + -0.4 -0.8y + y2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 -0.8y + y2 = -0.4 The y term is -0.8y. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8y + 0.16 + y2 = -0.4 + 0.16 Reorder the terms: 0.16 + -0.8y + y2 = -0.4 + 0.16 Combine like terms: -0.4 + 0.16 = -0.24 0.16 + -0.8y + y2 = -0.24 Factor a perfect square on the left side: (y + -0.4)(y + -0.4) = -0.24 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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