So all I have to do now is cross multiply and solve for x right? Also when that happens, how do I factor the x^3? What do I do?
Yes, that's all you do. And since I made that error, the estimate I gave you last night of 0.0017 for x will be slightly lower. I have recalculated and I obtained 0.001671 and although that's too many significant figures you almost must use all of them when you check the answer to make it come out right with all of those cubed and squared terms. I checked it also and it gave me exactly 4.2E-6 for Keq so I'm comfortable with that number.
How do I factor it? I didn't. I went looking on the web for a cubic equation calculator and used that.
But you can also do it by successive iterations and I did that too. It only took two estimates. It's done this way.
Take the equation and simplify it to
4X^3 = 4.2E-6
X^3 = 0.00173 for the first estimate. Then
4.2E-6 = 4X^3/(0.07-2x)^2
Substitute that first estimate of 0.00173 (for the denominator only) and solve for X and I get 0.00167 for x.
To solve a problem involving cross multiplication, you'll need to follow a few steps. Let's break it down step by step:
1. Cross multiplication: Multiplying the numerator of one fraction with the denominator of the other fraction, and vice versa, we get an equation in the form of "a/b = c/d." For example, if you have the equation (3/5) = (x/7), you would cross multiply to obtain 3 * 7 = 5 * x.
2. Solve for x: After cross multiplying, you'll have an equation in the form of a linear equation. In our previous example, you would have 21 = 5x. Now you can solve this equation to find the value of x. Divide both sides of the equation by 5, and you get x = 21/5 or x = 4.2.
Regarding factoring a polynomial containing x^3, there are various methods you can apply, depending on the specific polynomial. One approach is to use the factoring by grouping method. Here's an example:
Suppose you have the polynomial x^3 + 3x^2 + 2x + 6. You can begin factoring by grouping the terms:
(x^3 + 3x^2) + (2x + 6)
Now, factor out the common terms from each group:
x^2(x + 3) + 2(x + 3)
Notice that both terms have a common factor of (x + 3). So, you can further factor out (x + 3) to obtain the final factored form:
(x + 3)(x^2 + 2)
Therefore, the factored form of the polynomial x^3 + 3x^2 + 2x + 6 is (x + 3)(x^2 + 2).
Remember, factoring methods can vary depending on the polynomial you're working with, so it's helpful to familiarize yourself with different factorization techniques.