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Simplifying 10x(x2 + -4) + 2x(x2 + 4) = 0 Reorder the terms: 10x(-4 + x2) + 2x(x2 + 4) = 0 (-4 * 10x + x2 * 10x) + 2x(x2 + 4) = 0 (-40x + 10x3) + 2x(x2 + 4) = 0 Reorder the terms: -40x + 10x3 + 2x(4 + x2) = 0 -40x + 10x3 + (4 * 2x + x2 * 2x) = 0 -40x + 10x3 + (8x + 2x3) = 0 Reorder the terms: -40x + 8x + 10x3 + 2x3 = 0 Combine like terms: -40x + 8x = -32x -32x + 10x3 + 2x3 = 0 Combine like terms: 10x3 + 2x3 = 12x3 -32x + 12x3 = 0 Solving -32x + 12x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-8 + 3x2) = 0 Ignore the factor 4.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 '(-8 + 3x2)' equal to zero and attempt to solve: Simplifying -8 + 3x2 = 0 Solving -8 + 3x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 3x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3x2 = 0 + 8 3x2 = 0 + 8 Combine like terms: 0 + 8 = 8 3x2 = 8 Divide each side by '3'. x2 = 2.666666667 Simplifying x2 = 2.666666667 Take the square root of each side: x = {-1.632993162, 1.632993162}Solution
x = {0, -1.632993162, 1.632993162}
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