Question

Solve the equations by factoring 4x^2=13x

Answer 1

4x^2-13x =0
a=4
b=-13
c=0
x=0

Answer 2

We were given the following expression:

`4x^2=13x`

We need to solve it by factoring, this means that we need to find a way to rewrite the expression in such a way that we can determine the roots. The way we will factor is by using a common factor between the two terms, that way the expression will be reduced, and we will be able to immediately determine the roots. This is done below:

`\begin{gathered} 4x^2=13x \\ 4x^2-13x=13x-13x \\ 4x^2-13x=0 \end{gathered}`

There is a common factor "x" between the two terms, therefore we can rewrite it:

`x(4x-13)=0`

The left side of the equation is formed by the product of two terms, while the right side is equal to 0. This means that there are two possibilities that make this equation valid, they are shown below:

`\begin{gathered} x=0 \\ 4x-13=0 \end{gathered}`

With this we can determine the first root, which is x = 0. Now we need to solve the second equation, in order to determine the second root:

`\begin{gathered} 4x-13=0 \\ 4x=13 \\ x=(13)/(4) \end{gathered}`

With this, we were able to determine both roots, which are:

x = 0 and x = 13/4.