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Simplifying (y2 + -2y + 4)(y2 + 2y + 4) = 0 Reorder the terms: (4 + -2y + y2)(y2 + 2y + 4) = 0 Reorder the terms: (4 + -2y + y2)(4 + 2y + y2) = 0 Multiply (4 + -2y + y2) * (4 + 2y + y2) (4(4 + 2y + y2) + -2y * (4 + 2y + y2) + y2(4 + 2y + y2)) = 0 ((4 * 4 + 2y * 4 + y2 * 4) + -2y * (4 + 2y + y2) + y2(4 + 2y + y2)) = 0 ((16 + 8y + 4y2) + -2y * (4 + 2y + y2) + y2(4 + 2y + y2)) = 0 (16 + 8y + 4y2 + (4 * -2y + 2y * -2y + y2 * -2y) + y2(4 + 2y + y2)) = 0 (16 + 8y + 4y2 + (-8y + -4y2 + -2y3) + y2(4 + 2y + y2)) = 0 (16 + 8y + 4y2 + -8y + -4y2 + -2y3 + (4 * y2 + 2y * y2 + y2 * y2)) = 0 (16 + 8y + 4y2 + -8y + -4y2 + -2y3 + (4y2 + 2y3 + y4)) = 0 Reorder the terms: (16 + 8y + -8y + 4y2 + -4y2 + 4y2 + -2y3 + 2y3 + y4) = 0 Combine like terms: 8y + -8y = 0 (16 + 0 + 4y2 + -4y2 + 4y2 + -2y3 + 2y3 + y4) = 0 (16 + 4y2 + -4y2 + 4y2 + -2y3 + 2y3 + y4) = 0 Combine like terms: 4y2 + -4y2 = 0 (16 + 0 + 4y2 + -2y3 + 2y3 + y4) = 0 (16 + 4y2 + -2y3 + 2y3 + y4) = 0 Combine like terms: -2y3 + 2y3 = 0 (16 + 4y2 + 0 + y4) = 0 (16 + 4y2 + y4) = 0 Solving 16 + 4y2 + y4 = 0 Solving for variable 'y'. Begin completing the square. Move the constant term to the right: Add '-16' to each side of the equation. 16 + 4y2 + -16 + y4 = 0 + -16 Reorder the terms: 16 + -16 + 4y2 + y4 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + 4y2 + y4 = 0 + -16 4y2 + y4 = 0 + -16 Combine like terms: 0 + -16 = -16 4y2 + y4 = -16 The y term is 4y2. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4y2 + 4 + y4 = -16 + 4 Reorder the terms: 4 + 4y2 + y4 = -16 + 4 Combine like terms: -16 + 4 = -12 4 + 4y2 + y4 = -12 Factor a perfect square on the left side: (y2 + 2)(y2 + 2) = -12 Can't calculate square root of the right side. The solution to this equation could not be determined.
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