how do i solve this?
x(1+2x)= (2x-1)(x-2)
multiply out both sides. Then, gather like terms into quadratic form.
ax^2 +bx +c=0
Then, factor, or use the quadratic formula.
what does it mean to multiply out both sides
To solve this equation, we need to simplify both sides and then isolate the variable x.
Let's start by simplifying the equation step by step:
1. Expand the left side:
x(1 + 2x) = x + 2x^2
2. Expand the right side:
(2x - 1)(x - 2) = 2x^2 - 5x + 2
Now our equation becomes:
x + 2x^2 = 2x^2 - 5x + 2
Next, let's collect the like terms on one side:
x + 2x^2 - 2x^2 + 5x - 2 = 0
Simplifying further, we have:
6x - 2 = 0
Lastly, let's isolate the variable x by moving the constant term to the other side:
6x - 2 + 2 = 0 + 2
6x = 2
Finally, divide both sides by 6 to solve for x:
(6x)/6 = 2/6
x = 1/3
So the solution to the equation x(1 + 2x) = (2x - 1)(x - 2) is x = 1/3.