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Simplifying 100y2 + 160y + 128 = 0 Reorder the terms: 128 + 160y + 100y2 = 0 Solving 128 + 160y + 100y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '4'. 4(32 + 40y + 25y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(32 + 40y + 25y2)' equal to zero and attempt to solve: Simplifying 32 + 40y + 25y2 = 0 Solving 32 + 40y + 25y2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 1.28 + 1.6y + y2 = 0 Move the constant term to the right: Add '-1.28' to each side of the equation. 1.28 + 1.6y + -1.28 + y2 = 0 + -1.28 Reorder the terms: 1.28 + -1.28 + 1.6y + y2 = 0 + -1.28 Combine like terms: 1.28 + -1.28 = 0.00 0.00 + 1.6y + y2 = 0 + -1.28 1.6y + y2 = 0 + -1.28 Combine like terms: 0 + -1.28 = -1.28 1.6y + y2 = -1.28 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 = -1.28 + 0.64 Reorder the terms: 0.64 + 1.6y + y2 = -1.28 + 0.64 Combine like terms: -1.28 + 0.64 = -0.64 0.64 + 1.6y + y2 = -0.64 Factor a perfect square on the left side: (y + 0.8)(y + 0.8) = -0.64 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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