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Simplifying 0 = 3x4 + -24x2 + 144 Reorder the terms: 0 = 144 + -24x2 + 3x4 Solving 0 = 144 + -24x2 + 3x4 Solving for variable 'x'. Combine like terms: 0 + -144 = -144 -144 + 24x2 + -3x4 = 144 + -24x2 + 3x4 + -144 + 24x2 + -3x4 Reorder the terms: -144 + 24x2 + -3x4 = 144 + -144 + -24x2 + 24x2 + 3x4 + -3x4 Combine like terms: 144 + -144 = 0 -144 + 24x2 + -3x4 = 0 + -24x2 + 24x2 + 3x4 + -3x4 -144 + 24x2 + -3x4 = -24x2 + 24x2 + 3x4 + -3x4 Combine like terms: -24x2 + 24x2 = 0 -144 + 24x2 + -3x4 = 0 + 3x4 + -3x4 -144 + 24x2 + -3x4 = 3x4 + -3x4 Combine like terms: 3x4 + -3x4 = 0 -144 + 24x2 + -3x4 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-48 + 8x2 + -1x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-48 + 8x2 + -1x4)' equal to zero and attempt to solve: Simplifying -48 + 8x2 + -1x4 = 0 Solving -48 + 8x2 + -1x4 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 48 + -8x2 + x4 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + -8x2 + -48 + x4 = 0 + -48 Reorder the terms: 48 + -48 + -8x2 + x4 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -8x2 + x4 = 0 + -48 -8x2 + x4 = 0 + -48 Combine like terms: 0 + -48 = -48 -8x2 + x4 = -48 The x term is -8x2. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x2 + 16 + x4 = -48 + 16 Reorder the terms: 16 + -8x2 + x4 = -48 + 16 Combine like terms: -48 + 16 = -32 16 + -8x2 + x4 = -32 Factor a perfect square on the left side: (x2 + -4)(x2 + -4) = -32 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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