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Simplifying 15x4 + -27x2 + 15 = 0 Reorder the terms: 15 + -27x2 + 15x4 = 0 Solving 15 + -27x2 + 15x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(5 + -9x2 + 5x4) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -9x2 + 5x4)' equal to zero and attempt to solve: Simplifying 5 + -9x2 + 5x4 = 0 Solving 5 + -9x2 + 5x4 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + -1.8x2 + x4 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1.8x2 + -1 + x4 = 0 + -1 Reorder the terms: 1 + -1 + -1.8x2 + x4 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1.8x2 + x4 = 0 + -1 -1.8x2 + x4 = 0 + -1 Combine like terms: 0 + -1 = -1 -1.8x2 + x4 = -1 The x term is -1.8x2. Take half its coefficient (-0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. -1.8x2 + 0.81 + x4 = -1 + 0.81 Reorder the terms: 0.81 + -1.8x2 + x4 = -1 + 0.81 Combine like terms: -1 + 0.81 = -0.19 0.81 + -1.8x2 + x4 = -0.19 Factor a perfect square on the left side: (x2 + -0.9)(x2 + -0.9) = -0.19 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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