Answer:
Therefore, the value of x in the equation 4x^2(x + 3) = 8 is x = -1/2.
Explanation:
To find the value of x in the equation 4x^2(x + 3) = 8, we need to solve for x. Let's break down the equation step by step.
First, let's simplify the equation by distributing the 4x^2 term:
4x^2(x + 3) = 8
4x^2 * x + 4x^2 * 3 = 8
4x^3 + 12x^2 = 8
Next, let's rearrange the equation to bring all terms to one side:
4x^3 + 12x^2 - 8 = 0
Now, we have a cubic equation. Unfortunately, there is no general formula to solve cubic equations like there is for quadratic equations. However, we can use numerical methods or factoring techniques to approximate or find possible solutions.
One common approach is to use the Rational Root Theorem, which states that if a rational number p/q is a root of a polynomial equation with integer coefficients, then p must be a factor of the constant term (in this case, -8), and q must be a factor of the leading coefficient (in this case, 4).
The factors of -8 are ±1, ±2, ±4, and ±8.
The factors of 4 are ±1 and ±2.
So, the possible rational roots of the equation are:
±1/1, ±1/2, ±1/4, ±1/8,
±2/1, ±2/2 (=1), ±2/4 (=1/2), ±2/8 (=1/4).
We can now test these possible roots by substituting them into the equation and checking if they satisfy it. By doing so, we find that x = -1/2 is a solution.