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Simplifying 100x4 + 96x2 + 40 = 0 Reorder the terms: 40 + 96x2 + 100x4 = 0 Solving 40 + 96x2 + 100x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(10 + 24x2 + 25x4) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(10 + 24x2 + 25x4)' equal to zero and attempt to solve: Simplifying 10 + 24x2 + 25x4 = 0 Solving 10 + 24x2 + 25x4 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.4 + 0.96x2 + x4 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 0.96x2 + -0.4 + x4 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 0.96x2 + x4 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 0.96x2 + x4 = 0 + -0.4 0.96x2 + x4 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 0.96x2 + x4 = -0.4 The x term is 0.96x2. Take half its coefficient (0.48). Square it (0.2304) and add it to both sides. Add '0.2304' to each side of the equation. 0.96x2 + 0.2304 + x4 = -0.4 + 0.2304 Reorder the terms: 0.2304 + 0.96x2 + x4 = -0.4 + 0.2304 Combine like terms: -0.4 + 0.2304 = -0.1696 0.2304 + 0.96x2 + x4 = -0.1696 Factor a perfect square on the left side: (x2 + 0.48)(x2 + 0.48) = -0.1696 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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