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Simplifying 8 = 48x2 + 40x4 Solving 8 = 48x2 + 40x4 Solving for variable 'x'. Reorder the terms: 8 + -48x2 + -40x4 = 48x2 + -48x2 + 40x4 + -40x4 Combine like terms: 48x2 + -48x2 = 0 8 + -48x2 + -40x4 = 0 + 40x4 + -40x4 8 + -48x2 + -40x4 = 40x4 + -40x4 Combine like terms: 40x4 + -40x4 = 0 8 + -48x2 + -40x4 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(1 + -6x2 + -5x4) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(1 + -6x2 + -5x4)' equal to zero and attempt to solve: Simplifying 1 + -6x2 + -5x4 = 0 Solving 1 + -6x2 + -5x4 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + 1.2x2 + x4 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + 1.2x2 + 0.2 + x4 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + 1.2x2 + x4 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + 1.2x2 + x4 = 0 + 0.2 1.2x2 + x4 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 1.2x2 + x4 = 0.2 The x term is 1.2x2. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x2 + 0.36 + x4 = 0.2 + 0.36 Reorder the terms: 0.36 + 1.2x2 + x4 = 0.2 + 0.36 Combine like terms: 0.2 + 0.36 = 0.56 0.36 + 1.2x2 + x4 = 0.56 Factor a perfect square on the left side: (x2 + 0.6)(x2 + 0.6) = 0.56 Calculate the square root of the right side: 0.748331477 Break this problem into two subproblems by setting (x2 + 0.6) equal to 0.748331477 and -0.748331477.Subproblem 1
x2 + 0.6 = 0.748331477 Simplifying x2 + 0.6 = 0.748331477 Reorder the terms: 0.6 + x2 = 0.748331477 Solving 0.6 + x2 = 0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x2 = 0.748331477 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x2 = 0.748331477 + -0.6 x2 = 0.748331477 + -0.6 Combine like terms: 0.748331477 + -0.6 = 0.148331477 x2 = 0.148331477 Simplifying x2 = 0.148331477 Take the square root of each side: x = {-0.385138257, 0.385138257}Subproblem 2
x2 + 0.6 = -0.748331477 Simplifying x2 + 0.6 = -0.748331477 Reorder the terms: 0.6 + x2 = -0.748331477 Solving 0.6 + x2 = -0.748331477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x2 = -0.748331477 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x2 = -0.748331477 + -0.6 x2 = -0.748331477 + -0.6 Combine like terms: -0.748331477 + -0.6 = -1.348331477 x2 = -1.348331477 Simplifying x2 = -1.348331477 Reorder the terms: 1.348331477 + x2 = -1.348331477 + 1.348331477 Combine like terms: -1.348331477 + 1.348331477 = 0.000000000 1.348331477 + 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. 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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