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Simplifying (-3x4 + -1) + -1(5x4 + 4x2 + 6) = 0 Reorder the terms: (-1 + -3x4) + -1(5x4 + 4x2 + 6) = 0 Remove parenthesis around (-1 + -3x4) -1 + -3x4 + -1(5x4 + 4x2 + 6) = 0 Reorder the terms: -1 + -3x4 + -1(6 + 4x2 + 5x4) = 0 -1 + -3x4 + (6 * -1 + 4x2 * -1 + 5x4 * -1) = 0 -1 + -3x4 + (-6 + -4x2 + -5x4) = 0 Reorder the terms: -1 + -6 + -4x2 + -3x4 + -5x4 = 0 Combine like terms: -1 + -6 = -7 -7 + -4x2 + -3x4 + -5x4 = 0 Combine like terms: -3x4 + -5x4 = -8x4 -7 + -4x2 + -8x4 = 0 Solving -7 + -4x2 + -8x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(7 + 4x2 + 8x4) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(7 + 4x2 + 8x4)' equal to zero and attempt to solve: Simplifying 7 + 4x2 + 8x4 = 0 Solving 7 + 4x2 + 8x4 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 0.875 + 0.5x2 + x4 = 0 Move the constant term to the right: Add '-0.875' to each side of the equation. 0.875 + 0.5x2 + -0.875 + x4 = 0 + -0.875 Reorder the terms: 0.875 + -0.875 + 0.5x2 + x4 = 0 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + 0.5x2 + x4 = 0 + -0.875 0.5x2 + x4 = 0 + -0.875 Combine like terms: 0 + -0.875 = -0.875 0.5x2 + x4 = -0.875 The x term is 0.5x2. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x2 + 0.0625 + x4 = -0.875 + 0.0625 Reorder the terms: 0.0625 + 0.5x2 + x4 = -0.875 + 0.0625 Combine like terms: -0.875 + 0.0625 = -0.8125 0.0625 + 0.5x2 + x4 = -0.8125 Factor a perfect square on the left side: (x2 + 0.25)(x2 + 0.25) = -0.8125 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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