Question

Solve the equation by factoring.

4x2 - 7x = 2

Answer 1

\[4x^2-7x=2\]

Answer 2

first step is to subtract 2 from both sides

Answer 3

ok then divide by 4

Answer 4

If it is to the power of whatever you put ^

Answer 5

for example x^2;)

Answer 6

do i do formula \[b+-\sqrt{b^2-4ac}/2a\]

Answer 7

does anyone know the answer

Answer 8

ax^2+bx+c=0
4x^2-7x-2=0
Then plug in a b and c

Answer 9

7+ the square root of (7^2-4*4*2) divided by 2*4

Answer 10

and 7- the square root of (7^2-4*4*2) divided by 2*4

Answer 11

which is

Answer 12

Do both then plug them in

Answer 13

?

Answer 14

Since we want to solve this by factoring, one side of the equation must be zero. That's a key step.

\[4x^2-7x=2\]
\[4x^2-7x-2=2-2\] Subtract both sides by 2 to make the right side 0.
\[4x^2-7x-2=0\]

Answer 15

yes i got that! then what

Answer 16

Next step is to factor out the trinomial on the left side.

Answer 17

To do that, think of two numbers such that the product is -8 and sum is -7.

Answer 18

The correct combination is -8 and 1. Since (-8)(1)=-8 and (-8)+(1)=-7.

Answer 19

Now we will replace the middle term of the trinomial by the two numbers we found.

\[4x^2-7x-2=0\]
\[4x^2-8x+1x-2=0\]

Answer 20

Grouping them into two...

\[(4x^2-8x)+(x-2)=0\]

Factor out 4x on the first parenthesis, and factor out 1 on the second parenthesis...
\[4x(x-2)+1(x-2)=0\]

Answer 21

Notice that we can do one final factorization by pulling out the common factor (x-2). This gives us...

\[(x-2)(4x+1)=0\]

Answer 22

One last step. Set each factor equal to zero and solve for x.

x-2= 0
x=2

4x+1=0
4x=-1
x=-1/4

So our final answers are x = 2 and x=-1/4.

Hope this helps.

Answer 23

yes thank you so much!

Answer 24

You're welcome. Thank you.