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Simplifying (8x2 + -27)(48x2) = 0 Reorder the terms: (-27 + 8x2)(48x2) = 0 Remove parenthesis around (48x2) (-27 + 8x2) * 48x2 = 0 Reorder the terms for easier multiplication: 48x2(-27 + 8x2) = 0 (-27 * 48x2 + 8x2 * 48x2) = 0 (-1296x2 + 384x4) = 0 Solving -1296x2 + 384x4 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '48x2'. 48x2(-27 + 8x2) = 0 Ignore the factor 48.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
Set the factor '(-27 + 8x2)' equal to zero and attempt to solve: Simplifying -27 + 8x2 = 0 Solving -27 + 8x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '27' to each side of the equation. -27 + 27 + 8x2 = 0 + 27 Combine like terms: -27 + 27 = 0 0 + 8x2 = 0 + 27 8x2 = 0 + 27 Combine like terms: 0 + 27 = 27 8x2 = 27 Divide each side by '8'. x2 = 3.375 Simplifying x2 = 3.375 Take the square root of each side: x = {-1.837117307, 1.837117307}Solution
x = {0, -1.837117307, 1.837117307}
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