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Simplifying 3x4 + -18x2 + 75 = 0 Reorder the terms: 75 + -18x2 + 3x4 = 0 Solving 75 + -18x2 + 3x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(25 + -6x2 + x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(25 + -6x2 + x4)' equal to zero and attempt to solve: Simplifying 25 + -6x2 + x4 = 0 Solving 25 + -6x2 + x4 = 0 Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + -6x2 + -25 + x4 = 0 + -25 Reorder the terms: 25 + -25 + -6x2 + x4 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -6x2 + x4 = 0 + -25 -6x2 + x4 = 0 + -25 Combine like terms: 0 + -25 = -25 -6x2 + x4 = -25 The x term is -6x2. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x2 + 9 + x4 = -25 + 9 Reorder the terms: 9 + -6x2 + x4 = -25 + 9 Combine like terms: -25 + 9 = -16 9 + -6x2 + x4 = -16 Factor a perfect square on the left side: (x2 + -3)(x2 + -3) = -16 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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