.000006 .000002
_____ = _________
x² (4-x)²
To solve the given equation, we need to simplify the expression on the left side of the equation. Let's start by simplifying the denominators.
To simplify x², we don't need to do anything since it's already in its simplest form.
Now, let's simplify (4-x)². We can simplify this expression by multiplying it out as (4-x)(4-x). Using the FOIL method (First, Outer, Inner, Last), we get:
(4-x)(4-x) = 4 * 4 + 4 * (-x) + (-x) * 4 + (-x) * (-x)
= 16 - 4x - 4x + x²
= 16 - 8x + x²
So the expression (4-x)² simplifies to 16 - 8x + x².
Now, we can substitute the simplified forms of the denominators back into the original equation:
(.000006) / x² = (.000002) / (16 - 8x + x²)
To further simplify the equation, we can cross-multiply:
(.000006) * (16 - 8x + x²) = (.000002) * x²
Simplifying further, we get:
(.000096 - .000048x + .000006x²) = .000002x²
Next, we can move all the terms to one side of the equation to get a quadratic equation in standard form:
.000006x² + .000048x + .000096 - .000002x² = 0
Now, we have a quadratic equation that can be solved using various methods such as factoring, completing the square, or using the quadratic formula.
To solve this equation, we gather like terms:
.000004x² + .000048x + .000096 = 0
Now, we can use methods like factoring, completing the square, or the quadratic formula to find the solutions for x.