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Simplifying 4y2 + 10 = 4y Reorder the terms: 10 + 4y2 = 4y Solving 10 + 4y2 = 4y Solving for variable 'y'. Reorder the terms: 10 + -4y + 4y2 = 4y + -4y Combine like terms: 4y + -4y = 0 10 + -4y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -2y + 2y2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(5 + -2y + 2y2)' equal to zero and attempt to solve: Simplifying 5 + -2y + 2y2 = 0 Solving 5 + -2y + 2y2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 2.5 + -1y + y2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1y + -2.5 + y2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1y + y2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1y + y2 = 0 + -2.5 -1y + y2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1y + y2 = -2.5 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 = -2.5 + 0.25 Reorder the terms: 0.25 + -1y + y2 = -2.5 + 0.25 Combine like terms: -2.5 + 0.25 = -2.25 0.25 + -1y + y2 = -2.25 Factor a perfect square on the left side: (y + -0.5)(y + -0.5) = -2.25 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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