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Simplifying (3x4 + -5x2 + -4)(-3x3) = 0 Reorder the terms: (-4 + -5x2 + 3x4)(-3x3) = 0 Remove parenthesis around (-3x3) (-4 + -5x2 + 3x4) * -3x3 = 0 Reorder the terms for easier multiplication: -3x3(-4 + -5x2 + 3x4) = 0 (-4 * -3x3 + -5x2 * -3x3 + 3x4 * -3x3) = 0 (12x3 + 15x5 + -9x7) = 0 Solving 12x3 + 15x5 + -9x7 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3x3'. 3x3(4 + 5x2 + -3x4) = 0 Ignore the factor 3.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 '(4 + 5x2 + -3x4)' equal to zero and attempt to solve: Simplifying 4 + 5x2 + -3x4 = 0 Solving 4 + 5x2 + -3x4 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1.333333333 + -1.666666667x2 + x4 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -1.666666667x2 + 1.333333333 + x4 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -1.666666667x2 + x4 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -1.666666667x2 + x4 = 0 + 1.333333333 -1.666666667x2 + x4 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -1.666666667x2 + x4 = 1.333333333 The x term is -1.666666667x2. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667x2 + 0.6944444447 + x4 = 1.333333333 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667x2 + x4 = 1.333333333 + 0.6944444447 Combine like terms: 1.333333333 + 0.6944444447 = 2.0277777777 0.6944444447 + -1.666666667x2 + x4 = 2.0277777777 Factor a perfect square on the left side: (x2 + -0.8333333335)(x2 + -0.8333333335) = 2.0277777777 Calculate the square root of the right side: 1.424000624 Break this problem into two subproblems by setting (x2 + -0.8333333335) equal to 1.424000624 and -1.424000624.Subproblem 1
x2 + -0.8333333335 = 1.424000624 Simplifying x2 + -0.8333333335 = 1.424000624 Reorder the terms: -0.8333333335 + x2 = 1.424000624 Solving -0.8333333335 + x2 = 1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x2 = 1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x2 = 1.424000624 + 0.8333333335 x2 = 1.424000624 + 0.8333333335 Combine like terms: 1.424000624 + 0.8333333335 = 2.2573339575 x2 = 2.2573339575 Simplifying x2 = 2.2573339575 Take the square root of each side: x = {-1.502442664, 1.502442664}Subproblem 2
x2 + -0.8333333335 = -1.424000624 Simplifying x2 + -0.8333333335 = -1.424000624 Reorder the terms: -0.8333333335 + x2 = -1.424000624 Solving -0.8333333335 + x2 = -1.424000624 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + x2 = -1.424000624 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + x2 = -1.424000624 + 0.8333333335 x2 = -1.424000624 + 0.8333333335 Combine like terms: -1.424000624 + 0.8333333335 = -0.5906672905 x2 = -0.5906672905 Simplifying x2 = -0.5906672905 Reorder the terms: 0.5906672905 + x2 = -0.5906672905 + 0.5906672905 Combine like terms: -0.5906672905 + 0.5906672905 = 0.0000000000 0.5906672905 + x2 = 0.0000000000 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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