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Simplifying 4y(5y + -8) + 28 = 0 Reorder the terms: 4y(-8 + 5y) + 28 = 0 (-8 * 4y + 5y * 4y) + 28 = 0 (-32y + 20y2) + 28 = 0 Reorder the terms: 28 + -32y + 20y2 = 0 Solving 28 + -32y + 20y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -8y + 5y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -8y + 5y2)' equal to zero and attempt to solve: Simplifying 7 + -8y + 5y2 = 0 Solving 7 + -8y + 5y2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.4 + -1.6y + y2 = 0 Move the constant term to the right: Add '-1.4' to each side of the equation. 1.4 + -1.6y + -1.4 + y2 = 0 + -1.4 Reorder the terms: 1.4 + -1.4 + -1.6y + y2 = 0 + -1.4 Combine like terms: 1.4 + -1.4 = 0.0 0.0 + -1.6y + y2 = 0 + -1.4 -1.6y + y2 = 0 + -1.4 Combine like terms: 0 + -1.4 = -1.4 -1.6y + y2 = -1.4 The y term is -1.6y. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6y + 0.64 + y2 = -1.4 + 0.64 Reorder the terms: 0.64 + -1.6y + y2 = -1.4 + 0.64 Combine like terms: -1.4 + 0.64 = -0.76 0.64 + -1.6y + y2 = -0.76 Factor a perfect square on the left side: (y + -0.8)(y + -0.8) = -0.76 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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