Question

Using graphing technology, approximate the solutions of 0.35x2 − 2.52x + 1.34 = 0.

x ≈ 0.12 and x ≈ 4.56

x ≈ 0.58 and x ≈ 6.62

x ≈ 1.17 and x ≈ 6.14

x ≈ 1.83 and x ≈ 4.84

Answer 1

@bradely could ya help ?

Answer 2

Do you have a graphing calculator?

Answer 3

no .-.

Answer 4

Oh boy. That's what they mean by using technology. If you are in a class that requires you to do something like this, you will definitely need one. You could, however, use the quadratic formula to find the roots. Do you know it?

Answer 5

its online, its a lesson they didnt mention it how annoying.
do they give that to me?

Answer 6

If they want you to use a graphing calculator or some other type of technology, then they wouldn't mention the quadratic formula. But you could use it to find the roots in a quadratic equation like this one that is otherwise unfactorable. You can factor anything quadratic with the quadratic formula. But you need to know it first. I'll type it in here and help you find your answer without a calculator, ok?

Answer 7

\[x=\frac{ -b \pm \sqrt{(b)^{2}-4ac} }{2a }\]

Answer 8

Does that look familiar?

Answer 9

yes!

Answer 10

Ok, then let's do this. It will work just fine for you...although you probably should get at least a Texas Instruments 30 or higher.

Answer 11

Can you fill in the formula yourself using the values from your equation or do you need help with it?

Answer 12

i can attempt hold on

Answer 13

just kidding decimals are satans numbers, please help lol

Answer 14

ok, I'll be right back...have to put my kids to bed. Hold on a sec...

Answer 15

Promise I'll be right back.

Answer 16

Ok, I'm back. I'll set it up for you, ok?

Answer 17

\[x=\frac{ 2.52\pm \sqrt{(-2.52)^{2}-4(.35)(1.34)} }{ 2(.35) }\]

Answer 18

That simplifies a bit to this:

Answer 19

\[x=\frac{ 2.52\pm \sqrt{6.3504-1.876} }{.7 }\]

Answer 20

Simplifying further will give you this:

Answer 21

\[x=\frac{ 2.52\pm \sqrt{4.4744} }{ .7 }\]

Answer 22

And then...

Answer 23

\[x=\frac{ 2.52\pm 2.17807 }{ .7 }\]

Answer 24

This is where you get your two values for x. You have a plus/minus. So the solutions can be found in this way:

Answer 25

\[x=\frac{ 2.52+2.17807 }{ .7 }\]and\[x=\frac{ 2.52-2.17807 }{ .7 }\]

Answer 26

Solving these two equations for your x values gives you 6.71153 and .488471

Answer 27

Keep in mind that your values are exact, but the closest ones to them are 6.62 and .58

Answer 28

And that's it!

Answer 29

And that's correct; I just did it on my own calculator.