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Simplifying (7x4 + 2x2 + -4) + -1(-1x4 + -3x2 + 6) = 0 Reorder the terms: (-4 + 2x2 + 7x4) + -1(-1x4 + -3x2 + 6) = 0 Remove parenthesis around (-4 + 2x2 + 7x4) -4 + 2x2 + 7x4 + -1(-1x4 + -3x2 + 6) = 0 Reorder the terms: -4 + 2x2 + 7x4 + -1(6 + -3x2 + -1x4) = 0 -4 + 2x2 + 7x4 + (6 * -1 + -3x2 * -1 + -1x4 * -1) = 0 -4 + 2x2 + 7x4 + (-6 + 3x2 + 1x4) = 0 Reorder the terms: -4 + -6 + 2x2 + 3x2 + 7x4 + 1x4 = 0 Combine like terms: -4 + -6 = -10 -10 + 2x2 + 3x2 + 7x4 + 1x4 = 0 Combine like terms: 2x2 + 3x2 = 5x2 -10 + 5x2 + 7x4 + 1x4 = 0 Combine like terms: 7x4 + 1x4 = 8x4 -10 + 5x2 + 8x4 = 0 Solving -10 + 5x2 + 8x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + 0.625x2 + x4 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.625x2 + 1.25 + x4 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.625x2 + x4 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.625x2 + x4 = 0 + 1.25 0.625x2 + x4 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.625x2 + x4 = 1.25 The x term is 0.625x2. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625x2 + 0.09765625 + x4 = 1.25 + 0.09765625 Reorder the terms: 0.09765625 + 0.625x2 + x4 = 1.25 + 0.09765625 Combine like terms: 1.25 + 0.09765625 = 1.34765625 0.09765625 + 0.625x2 + x4 = 1.34765625 Factor a perfect square on the left side: (x2 + 0.3125)(x2 + 0.3125) = 1.34765625 Calculate the square root of the right side: 1.160885976 Break this problem into two subproblems by setting (x2 + 0.3125) equal to 1.160885976 and -1.160885976.Subproblem 1
x2 + 0.3125 = 1.160885976 Simplifying x2 + 0.3125 = 1.160885976 Reorder the terms: 0.3125 + x2 = 1.160885976 Solving 0.3125 + x2 = 1.160885976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x2 = 1.160885976 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x2 = 1.160885976 + -0.3125 x2 = 1.160885976 + -0.3125 Combine like terms: 1.160885976 + -0.3125 = 0.848385976 x2 = 0.848385976 Simplifying x2 = 0.848385976 Take the square root of each side: x = {-0.921078702, 0.921078702}Subproblem 2
x2 + 0.3125 = -1.160885976 Simplifying x2 + 0.3125 = -1.160885976 Reorder the terms: 0.3125 + x2 = -1.160885976 Solving 0.3125 + x2 = -1.160885976 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + x2 = -1.160885976 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + x2 = -1.160885976 + -0.3125 x2 = -1.160885976 + -0.3125 Combine like terms: -1.160885976 + -0.3125 = -1.473385976 x2 = -1.473385976 Simplifying x2 = -1.473385976 Reorder the terms: 1.473385976 + x2 = -1.473385976 + 1.473385976 Combine like terms: -1.473385976 + 1.473385976 = 0.000000000 1.473385976 + x2 = 0.000000000 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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