(4.44e-2 - x) (8.06e-2 - x) / (0.331 + 2x)^2 = 1.80e-2

I need to rearrange this equation so that I can get a,b, and c, for the quadratic equation but I am not sure how to do this. Thank you for the help.

multpily both sides by (.331+2x)^2

now multiply out the left side, getting four terms. On the right, mupltiply all that square term out

Now, collect terms. Put them all on one side, you will have the quadratic form.

It is mostly algebra.

So I have to multiply (4.44e-2 -x )(8.06e-2 - x) by (0.331 + 2x)^2 or am I suppose to multiply 1.80e-2 by it?

To rearrange the equation in the form of a quadratic equation (ax^2 + bx + c = 0), we need to first expand the expression on the left side and simplify it. Then, we can compare it with the given value (1.80e-2) to find the coefficients of the quadratic equation.

Let's start by multiplying out the terms:

(4.44e-2 - x) * (8.06e-2 - x) = (0.331 + 2x)^2 * (1.80e-2)

Expanding the left side:

(4.44e-2 - x) * (8.06e-2 - x) = (0.331 + 2x) * (0.331 + 2x)

Using the distributive property, we can multiply each term:

(4.44e-2 * 8.06e-2) - (x * 8.06e-2) - (4.44e-2 * x) + (x^2)
= (0.331 * 0.331) + (0.331 * 2x) + (2x * 0.331) + (2x * 2x)

Now, simplify both sides:

(0.0358064 - 0.0806x - 0.0806x + x^2)
= (0.109561 + 0.662x + 0.662x + 4x^2)

Combine like terms:

0.0358064 - 0.1612x + x^2
= 0.109561 + 1.324x + 4x^2

Rearrange the equation by subtracting both sides by their respective terms:

0.0358064 - 0.109561 + x^2 - 4x^2 + 0.1612x - 1.324x = 0

Combine like terms again:

-3x^2 - 1.1628x - 0.0737546 = 0

Now, we have the equation in the form of a quadratic equation: ax^2 + bx + c = 0. Comparing it with the rearranged equation, we can identify the coefficients:

a = -3
b = -1.1628
c = -0.0737546

You can now use these coefficients to find the solutions to the quadratic equation using various methods, such as factoring, completing the square, or using the quadratic formula.