To solve this equation for x, we need to first simplify the left side of the equation:
4x^3 - 3x + 5 = 4
Next, we need to subtract 4 from both sides of the equation to isolate the variable:
4x^3 - 3x + 5 - 4 = 4 - 4 4x^3 - 3x + 1 = 0
Now we have a polynomial equation that we can try to solve. However, this equation may not have a simple solution. One common technique to solve cubic equations like this one is to use the Rational Root Theorem to find potential roots.
By the Rational Root Theorem, the possible rational roots of this equation are the factors of the constant term (1 in this case), divided by the factors of the leading coefficient (4 in this case). Therefore, the possible rational roots are ±1/4 or ±1.
By testing these possible roots using synthetic division or polynomial long division, we can determine if any of them are actual roots of the equation. If we find a root, we can then use polynomial division to factor the equation and find the other roots.
Without solving for the exact roots, this is the general process for solving a cubic equation like the one given.
To solve this equation for x, we need to first simplify the left side of the equation:
4x^3 - 3x + 5 = 4
Next, we need to subtract 4 from both sides of the equation to isolate the variable:
4x^3 - 3x + 5 - 4 = 4 - 4
4x^3 - 3x + 1 = 0
Now we have a polynomial equation that we can try to solve. However, this equation may not have a simple solution. One common technique to solve cubic equations like this one is to use the Rational Root Theorem to find potential roots.
By the Rational Root Theorem, the possible rational roots of this equation are the factors of the constant term (1 in this case), divided by the factors of the leading coefficient (4 in this case). Therefore, the possible rational roots are ±1/4 or ±1.
By testing these possible roots using synthetic division or polynomial long division, we can determine if any of them are actual roots of the equation. If we find a root, we can then use polynomial division to factor the equation and find the other roots.
Without solving for the exact roots, this is the general process for solving a cubic equation like the one given.