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Simplifying 4x7 + -2x3 + 48x5 = 0 Reorder the terms: -2x3 + 48x5 + 4x7 = 0 Solving -2x3 + 48x5 + 4x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x3'. 2x3(-1 + 24x2 + 2x4) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x3' equal to zero and attempt to solve: Simplifying x3 = 0 Solving x3 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x3 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-1 + 24x2 + 2x4)' equal to zero and attempt to solve: Simplifying -1 + 24x2 + 2x4 = 0 Solving -1 + 24x2 + 2x4 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -0.5 + 12x2 + x4 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 12x2 + 0.5 + x4 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 12x2 + x4 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 12x2 + x4 = 0 + 0.5 12x2 + x4 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 12x2 + x4 = 0.5 The x term is 12x2. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x2 + 36 + x4 = 0.5 + 36 Reorder the terms: 36 + 12x2 + x4 = 0.5 + 36 Combine like terms: 0.5 + 36 = 36.5 36 + 12x2 + x4 = 36.5 Factor a perfect square on the left side: (x2 + 6)(x2 + 6) = 36.5 Calculate the square root of the right side: 6.041522987 Break this problem into two subproblems by setting (x2 + 6) equal to 6.041522987 and -6.041522987.Subproblem 1
x2 + 6 = 6.041522987 Simplifying x2 + 6 = 6.041522987 Reorder the terms: 6 + x2 = 6.041522987 Solving 6 + x2 = 6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = 6.041522987 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = 6.041522987 + -6 x2 = 6.041522987 + -6 Combine like terms: 6.041522987 + -6 = 0.041522987 x2 = 0.041522987 Simplifying x2 = 0.041522987 Take the square root of each side: x = {-0.203771899, 0.203771899}Subproblem 2
x2 + 6 = -6.041522987 Simplifying x2 + 6 = -6.041522987 Reorder the terms: 6 + x2 = -6.041522987 Solving 6 + x2 = -6.041522987 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x2 = -6.041522987 + -6 Combine like terms: 6 + -6 = 0 0 + x2 = -6.041522987 + -6 x2 = -6.041522987 + -6 Combine like terms: -6.041522987 + -6 = -12.041522987 x2 = -12.041522987 Simplifying x2 = -12.041522987 Reorder the terms: 12.041522987 + x2 = -12.041522987 + 12.041522987 Combine like terms: -12.041522987 + 12.041522987 = 0.000000000 12.041522987 + 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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