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Simplifying (6x3 + 7x + -5x)(x2 + -5) = 0 Reorder the terms: (7x + -5x + 6x3)(x2 + -5) = 0 Combine like terms: 7x + -5x = 2x (2x + 6x3)(x2 + -5) = 0 Reorder the terms: (2x + 6x3)(-5 + x2) = 0 Multiply (2x + 6x3) * (-5 + x2) (2x * (-5 + x2) + 6x3 * (-5 + x2)) = 0 ((-5 * 2x + x2 * 2x) + 6x3 * (-5 + x2)) = 0 ((-10x + 2x3) + 6x3 * (-5 + x2)) = 0 (-10x + 2x3 + (-5 * 6x3 + x2 * 6x3)) = 0 (-10x + 2x3 + (-30x3 + 6x5)) = 0 Combine like terms: 2x3 + -30x3 = -28x3 (-10x + -28x3 + 6x5) = 0 Solving -10x + -28x3 + 6x5 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2x'. 2x(-5 + -14x2 + 3x4) = 0 Factor a trinomial. 2x((-1 + -3x2)(5 + -1x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + -3x2)' equal to zero and attempt to solve: Simplifying -1 + -3x2 = 0 Solving -1 + -3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x2 = 0 + 1 -3x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3x2 = 1 Divide each side by '-3'. x2 = -0.3333333333 Simplifying x2 = -0.3333333333 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(5 + -1x2)' equal to zero and attempt to solve: Simplifying 5 + -1x2 = 0 Solving 5 + -1x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x2 = 0 + -5 -1x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -1x2 = -5 Divide each side by '-1'. x2 = 5 Simplifying x2 = 5 Take the square root of each side: x = {-2.236067978, 2.236067978}Solution
x = {0, -2.236067978, 2.236067978}
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