Question

Solve equation using both factoring and the quadratic formula 6x^2-13x-5=0

Answer 1

plug it into the quadratic formula

and check on mathway if its right

Answer 2

How about the factoring formula?

Answer 3

Sorry this took so long to type but here you go Trying to factor by splitting the middle term

2.1 Factoring 6x2-13x-5

The first term is, 6x2 its coefficient is 6 .
The middle term is, -13x its coefficient is -13 .
The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 6 • -5 = -30

Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -13 .

-30 + 1 = -29
-15 + 2 = -13 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -15 and 2
6x2 - 15x + 2x - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (2x-5)
Add up the last 2 terms, pulling out common factors :
1 • (2x-5)
Step-5 : Add up the four terms of step 4 :
(3x+1) • (2x-5)
Which is the desired factorization

Answer 4

There are two possible solutions to this problem x = -1/3 = -0.333 and
x = 5/2 = 2.500

Answer 5

Solve Quadratic Equation using the Quadratic Formula

4.3 Solving 6x2-13x-5 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x , the solution for Ax2+Bx+C = 0 , where A, B and C are numbers, often called coefficients, is given by :

- B ± √ B2-4AC
x = ————————
2A

In our case, A = 6
B = -13
C = -5

Accordingly, B2 - 4AC =
169 - (-120) =
289

Applying the quadratic formula :

13 ± √ 289
x = ——————
12

Can √ 289 be simplified ?

Yes! The prime factorization of 289 is
17•17
To be able to remove something from under the radical, there have to be 2 instances of it (because we are taking a square i.e. second root).

√ 289 = √ 17•17 =
± 17 • √ 1 =
± 17

So now we are looking at:
x = ( 13 ± 17) / 12

Two real solutions:

x =(13+√289)/12=(13+17)/12= 2.500

or:

x =(13-√289)/12=(13-17)/12= -0.333

Answer 6

Thank you so much I understand it now :)

Answer 7

Awesome!

Answer 8

Sorry it took so long to type

Answer 9

Welcome to OpenStudy please remember that you are not allowed to get direct answers here but are allowed to get answers with explanations like above. Keep on studying and follow these guidelines you will be fine!

Answer 10

Okay got you thanks