Question

Solve the following equation by factoring: 4x² - 15x = 4

Answer 1

Given:

`4x^2-15x=4`

Let's solve the equation by factoring,

Subtract 4 from both sides:

`\begin{gathered} 4x^2-15x-4=4-4 \\ \\ 4x^2-15x-4=0 \end{gathered}`

Now, let's factor by grouping.

Rewrite -15x as (x - 16x):

`4x^2+x-16x-4=0`

Now we have two groups:

`(4x^2+x)-16x-4=0`

Factor out x from the first group and factor out -4 from the second group:

`x(4x+1)-4(4x+1)=0`

Thus, we have the factors:

`(x-4)(4x+1)=0`

Set each factor to zero and solve for x:

`\begin{gathered} x-4=0 \\ Add\text{ 4 to both sides:} \\ x-4+4=0+4 \\ x=4 \\ \\ \\ 4x+1=0 \\ Subtract\text{ 1from both sides:} \\ 4x+1-1=0-1 \\ 4x=-1 \\ Divde\text{ both sides by 4:} \\ (4x)/(4)=-(1)/(4) \\ x=-(1)/(4) \end{gathered}`

Therefore, the solutions are:

`x=-(1)/(4)\text{ or x = 4}`

ANSWER: D

`x=-(1)/(4)\text{ or x = 4}`