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Simplifying 4y2 + -16y + 64 + y2 = y2 + 8y + 16 Reorder the terms: 64 + -16y + 4y2 + y2 = y2 + 8y + 16 Combine like terms: 4y2 + y2 = 5y2 64 + -16y + 5y2 = y2 + 8y + 16 Reorder the terms: 64 + -16y + 5y2 = 16 + 8y + y2 Solving 64 + -16y + 5y2 = 16 + 8y + y2 Solving for variable 'y'. Reorder the terms: 64 + -16 + -16y + -8y + 5y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2 Combine like terms: 64 + -16 = 48 48 + -16y + -8y + 5y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2 Combine like terms: -16y + -8y = -24y 48 + -24y + 5y2 + -1y2 = 16 + 8y + y2 + -16 + -8y + -1y2 Combine like terms: 5y2 + -1y2 = 4y2 48 + -24y + 4y2 = 16 + 8y + y2 + -16 + -8y + -1y2 Reorder the terms: 48 + -24y + 4y2 = 16 + -16 + 8y + -8y + y2 + -1y2 Combine like terms: 16 + -16 = 0 48 + -24y + 4y2 = 0 + 8y + -8y + y2 + -1y2 48 + -24y + 4y2 = 8y + -8y + y2 + -1y2 Combine like terms: 8y + -8y = 0 48 + -24y + 4y2 = 0 + y2 + -1y2 48 + -24y + 4y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 48 + -24y + 4y2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(12 + -6y + y2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(12 + -6y + y2)' equal to zero and attempt to solve: Simplifying 12 + -6y + y2 = 0 Solving 12 + -6y + y2 = 0 Begin completing the square. Move the constant term to the right: Add '-12' to each side of the equation. 12 + -6y + -12 + y2 = 0 + -12 Reorder the terms: 12 + -12 + -6y + y2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -6y + y2 = 0 + -12 -6y + y2 = 0 + -12 Combine like terms: 0 + -12 = -12 -6y + y2 = -12 The y term is -6y. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6y + 9 + y2 = -12 + 9 Reorder the terms: 9 + -6y + y2 = -12 + 9 Combine like terms: -12 + 9 = -3 9 + -6y + y2 = -3 Factor a perfect square on the left side: (y + -3)(y + -3) = -3 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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