All mathematics, especially algebra, is dependent on a sliding scale between positive, negative and neutral potentials (+/-/0).
3x + -8x + 4 (x ^ 3) = 0
Where X = SOMETHING CAN BE WRONG RIGHT AND NEITHER AT THE SAME TIME.
You ask to state this Algebraically:
3x + -8x + 4 (x ^ 3) = 0
Simplifying
3x + -8x + 4(x3) = 0
Combine like terms: 3x + -8x = -5x
-5x + 4x3 = 0
Solving
-5x + 4x3 = 0
Factor out the Greatest Common Factor (GCF), 'x'.
x(-5 + 4x2) = 0
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 = 0
Subproblem 2
Set the factor '(-5 + 4x2)' equal to zero and attempt to solve:
Simplifying
-5 + 4x2 = 0
Solving
-5 + 4x2 = 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 + 4x2 = 0 + 5
Combine like terms: -5 + 5 = 0
0 + 4x2 = 0 + 5
4x2 = 0 + 5
Combine like terms: 0 + 5 = 5
4x2 = 5
Divide each side by '4'.
x2 = 1.25
Simplifying
x2 = 1.25
Take the square root of each side:
x = {-1.118033989, 1.118033989}
Solution
x = {0, -1.118033989, 1.118033989}
The solution is +/-/0 SIMULTANEOUSLY
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