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Simplifying 0 = 1x4 + 0x3 + -8x2 + 0x + 0 Anything times zero is zero. 0 = 1x4 + 0x3 + -8x2 + 0x + 0 Anything times zero is zero. 0 = 1x4 + 0 + -8x2 + 0x + 0 Reorder the terms: 0 = 0 + 0 + 0 + -8x2 + 1x4 Combine like terms: 0 + 0 = 0 0 = 0 + 0 + -8x2 + 1x4 0 = 0 + -8x2 + 1x4 Remove the zero: 0 = -8x2 + 1x4 Solving 0 = -8x2 + 1x4 Solving for variable 'x'. Remove the zero: 8x2 + -1x4 = -8x2 + 1x4 + 8x2 + -1x4 Reorder the terms: 8x2 + -1x4 = -8x2 + 8x2 + 1x4 + -1x4 Combine like terms: -8x2 + 8x2 = 0 8x2 + -1x4 = 0 + 1x4 + -1x4 8x2 + -1x4 = 1x4 + -1x4 Combine like terms: 1x4 + -1x4 = 0 8x2 + -1x4 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(8 + -1x2) = 0Subproblem 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 '(8 + -1x2)' equal to zero and attempt to solve: Simplifying 8 + -1x2 = 0 Solving 8 + -1x2 = 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 + -1x2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x2 = 0 + -8 -1x2 = 0 + -8 Combine like terms: 0 + -8 = -8 -1x2 = -8 Divide each side by '-1'. x2 = 8 Simplifying x2 = 8 Take the square root of each side: x = {-2.828427125, 2.828427125}Solution
x = {0, -2.828427125, 2.828427125}
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