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Simplifying (x2 + -5)(x + -3)(x + 3) = 0 Reorder the terms: (-5 + x2)(x + -3)(x + 3) = 0 Reorder the terms: (-5 + x2)(-3 + x)(x + 3) = 0 Reorder the terms: (-5 + x2)(-3 + x)(3 + x) = 0 Multiply (-5 + x2) * (-3 + x) (-5(-3 + x) + x2(-3 + x))(3 + x) = 0 ((-3 * -5 + x * -5) + x2(-3 + x))(3 + x) = 0 ((15 + -5x) + x2(-3 + x))(3 + x) = 0 (15 + -5x + (-3 * x2 + x * x2))(3 + x) = 0 (15 + -5x + (-3x2 + x3))(3 + x) = 0 (15 + -5x + -3x2 + x3)(3 + x) = 0 Multiply (15 + -5x + -3x2 + x3) * (3 + x) (15(3 + x) + -5x * (3 + x) + -3x2 * (3 + x) + x3(3 + x)) = 0 ((3 * 15 + x * 15) + -5x * (3 + x) + -3x2 * (3 + x) + x3(3 + x)) = 0 ((45 + 15x) + -5x * (3 + x) + -3x2 * (3 + x) + x3(3 + x)) = 0 (45 + 15x + (3 * -5x + x * -5x) + -3x2 * (3 + x) + x3(3 + x)) = 0 (45 + 15x + (-15x + -5x2) + -3x2 * (3 + x) + x3(3 + x)) = 0 (45 + 15x + -15x + -5x2 + (3 * -3x2 + x * -3x2) + x3(3 + x)) = 0 (45 + 15x + -15x + -5x2 + (-9x2 + -3x3) + x3(3 + x)) = 0 (45 + 15x + -15x + -5x2 + -9x2 + -3x3 + (3 * x3 + x * x3)) = 0 (45 + 15x + -15x + -5x2 + -9x2 + -3x3 + (3x3 + x4)) = 0 Combine like terms: 15x + -15x = 0 (45 + 0 + -5x2 + -9x2 + -3x3 + 3x3 + x4) = 0 (45 + -5x2 + -9x2 + -3x3 + 3x3 + x4) = 0 Combine like terms: -5x2 + -9x2 = -14x2 (45 + -14x2 + -3x3 + 3x3 + x4) = 0 Combine like terms: -3x3 + 3x3 = 0 (45 + -14x2 + 0 + x4) = 0 (45 + -14x2 + x4) = 0 Solving 45 + -14x2 + x4 = 0 Solving for variable 'x'. Factor a trinomial. (5 + -1x2)(9 + -1x2) = 0 Factor a difference between two squares. (5 + -1x2)((3 + x)(3 + -1x)) = 0Subproblem 1
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}Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Subproblem 3
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-2.236067978, 2.236067978, -3, 3}
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