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Simplifying (2 + 4x + 8x2 + 7x3) + -1(-2 + -4x + -8x2 + 7x3) = 0 Remove parenthesis around (2 + 4x + 8x2 + 7x3) 2 + 4x + 8x2 + 7x3 + -1(-2 + -4x + -8x2 + 7x3) = 0 2 + 4x + 8x2 + 7x3 + (-2 * -1 + -4x * -1 + -8x2 * -1 + 7x3 * -1) = 0 2 + 4x + 8x2 + 7x3 + (2 + 4x + 8x2 + -7x3) = 0 Reorder the terms: 2 + 2 + 4x + 4x + 8x2 + 8x2 + 7x3 + -7x3 = 0 Combine like terms: 2 + 2 = 4 4 + 4x + 4x + 8x2 + 8x2 + 7x3 + -7x3 = 0 Combine like terms: 4x + 4x = 8x 4 + 8x + 8x2 + 8x2 + 7x3 + -7x3 = 0 Combine like terms: 8x2 + 8x2 = 16x2 4 + 8x + 16x2 + 7x3 + -7x3 = 0 Combine like terms: 7x3 + -7x3 = 0 4 + 8x + 16x2 + 0 = 0 4 + 8x + 16x2 = 0 Solving 4 + 8x + 16x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(1 + 2x + 4x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + 2x + 4x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 4x2 = 0 Solving 1 + 2x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 0.25 + 0.5x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 0.5x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 0.5x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 0.5x + x2 = 0 + -0.25 0.5x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 0.5x + x2 = -0.25 The x term is 0.5x. 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. 0.5x + 0.0625 + x2 = -0.25 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = -0.25 + 0.0625 Combine like terms: -0.25 + 0.0625 = -0.1875 0.0625 + 0.5x + x2 = -0.1875 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = -0.1875 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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