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Simplifying 15x4 + -12x2 + 3 = 0 Reorder the terms: 3 + -12x2 + 15x4 = 0 Solving 3 + -12x2 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(1 + -4x2 + 5x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(1 + -4x2 + 5x4)' equal to zero and attempt to solve: Simplifying 1 + -4x2 + 5x4 = 0 Solving 1 + -4x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.2 + -0.8x2 + x4 = 0 Move the constant term to the right: Add '-0.2' to each side of the equation. 0.2 + -0.8x2 + -0.2 + x4 = 0 + -0.2 Reorder the terms: 0.2 + -0.2 + -0.8x2 + x4 = 0 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + -0.8x2 + x4 = 0 + -0.2 -0.8x2 + x4 = 0 + -0.2 Combine like terms: 0 + -0.2 = -0.2 -0.8x2 + x4 = -0.2 The x term is -0.8x2. Take half its coefficient (-0.4). Square it (0.16) and add it to both sides. Add '0.16' to each side of the equation. -0.8x2 + 0.16 + x4 = -0.2 + 0.16 Reorder the terms: 0.16 + -0.8x2 + x4 = -0.2 + 0.16 Combine like terms: -0.2 + 0.16 = -0.04 0.16 + -0.8x2 + x4 = -0.04 Factor a perfect square on the left side: (x2 + -0.4)(x2 + -0.4) = -0.04 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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