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Simplifying 42y + -42y2 = 20 Solving 42y + -42y2 = 20 Solving for variable 'y'. Reorder the terms: -20 + 42y + -42y2 = 20 + -20 Combine like terms: 20 + -20 = 0 -20 + 42y + -42y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + 21y + -21y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + 21y + -21y2)' equal to zero and attempt to solve: Simplifying -10 + 21y + -21y2 = 0 Solving -10 + 21y + -21y2 = 0 Begin completing the square. Divide all terms by -21 the coefficient of the squared term: Divide each side by '-21'. 0.4761904762 + -1y + y2 = 0 Move the constant term to the right: Add '-0.4761904762' to each side of the equation. 0.4761904762 + -1y + -0.4761904762 + y2 = 0 + -0.4761904762 Reorder the terms: 0.4761904762 + -0.4761904762 + -1y + y2 = 0 + -0.4761904762 Combine like terms: 0.4761904762 + -0.4761904762 = 0.0000000000 0.0000000000 + -1y + y2 = 0 + -0.4761904762 -1y + y2 = 0 + -0.4761904762 Combine like terms: 0 + -0.4761904762 = -0.4761904762 -1y + y2 = -0.4761904762 The y term is -1y. 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. -1y + 0.25 + y2 = -0.4761904762 + 0.25 Reorder the terms: 0.25 + -1y + y2 = -0.4761904762 + 0.25 Combine like terms: -0.4761904762 + 0.25 = -0.2261904762 0.25 + -1y + y2 = -0.2261904762 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = -0.2261904762 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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