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Simplifying 2X(X^{2}+ -4X + 7) = 0 Reorder the terms: 2X(7 + -4X + X^{2}) = 0 (7 * 2X + -4X * 2X + X^{2}* 2X) = 0 (14X + -8X^{2}+ 2X^{3}) = 0 Solving 14X + -8X^{2}+ 2X^{3}= 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '2X'. 2X(7 + -4X + X^{2}) = 0 Ignore the factor 2.## Subproblem 1

Set the factor 'X' equal to zero and attempt to solve: Simplifying X = 0 Solving X = 0 Move all terms containing X to the left, all other terms to the right. Simplifying X = 0## Subproblem 2

Set the factor '(7 + -4X + X^{2})' equal to zero and attempt to solve: Simplifying 7 + -4X + X^{2}= 0 Solving 7 + -4X + X^{2}= 0 Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + -4X + -7 + X^{2}= 0 + -7 Reorder the terms: 7 + -7 + -4X + X^{2}= 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4X + X^{2}= 0 + -7 -4X + X^{2}= 0 + -7 Combine like terms: 0 + -7 = -7 -4X + X^{2}= -7 The X term is -4X. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4X + 4 + X^{2}= -7 + 4 Reorder the terms: 4 + -4X + X^{2}= -7 + 4 Combine like terms: -7 + 4 = -3 4 + -4X + X^{2}= -3 Factor a perfect square on the left side: (X + -2)(X + -2) = -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.## Solution

X = {0}

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