Question

What are the approximate solutions of 2x2 + 9x = 8 to the nearest hundredth?

x ≈ 1.22 and x ≈ 3.28

x ≈ −0.76 and x ≈ 5.26

x ≈ −1.22 and x ≈ −3.28

x ≈ −5.26 and x ≈ 0.76

Answer 1

@phi

Answer 2

Can you write this in standard form
\[ 2x^2 + 9x = 8 \]?

standard form is \( a x^2 + b x + c =0 \)

Answer 3

add -8 to both sides and simplify. what do you get ?

Answer 4

2x^2 + 9x - 8 = 8 - 8
x(2x + 9) = 8

Answer 5

1st line is ok.

but you should remember what we are trying to do: make it look like
a x^2 + bx + c =0

2x^2 + 9x -8 = 8-8
on the right side, 8-8 is 0 , so you can simplify to get

2x^2 + 9x -8 =0

that is standard form.

the only thing you had to do is replace 8-8 with 0.

Answer 6

now the hard part. To find the solutions you must use the quadratic formula

do you know it ?

Answer 7

no i dont ;/

Answer 8

it is complicated:

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

to use it you must identify the numbers that go with a, b , and c
match your equation
2x^2 + 9x + -8 =0
with
ax^2 + bx + c = 0

what is a, b and c ?

Answer 9

2, 9 and -8

Answer 10

@Mertsj

Answer 11

yes, now use those numbers to replace the letters in the formula.
can you do that ?

Answer 12

wherever you see an a, put in a 2 instead.
replace b with 9 and c with -8

Answer 13

but how the heck do i solve that LOL xD

Answer 14

The longest journey begins with a single step...

The first step is replace a with 2. I will do it to get you started
\[ x = \frac{-b ± \sqrt{b^2 - 4 ac}}{2a} \]
becomes
\[ x = \frac{-b ± \sqrt{b^2 - 4\cdot 2\cdot c}}{2 \cdot 2} \]

can you replace b with 9 ?
don't worry about solving anything. Just replace the letters with numbers.

Answer 15

NEVERMIND I GOT A CALCULATOR lol is it D?

Answer 16

@phi

Answer 17

to finish this problem.

replace b with 9 in
\[ x = \frac{-b ± \sqrt{b^2 - 4\cdot 2\cdot c}}{2 \cdot 2} \]
you get
\[ x = \frac{-9 ± \sqrt{9^2 - 4\cdot 2\cdot c}}{2 \cdot 2} \]

now replace c with -8 to get
\[x = \frac{-9 ± \sqrt{9^2 - 4\cdot 2\cdot -8}}{2 \cdot 2}\]

you need to know your order of operations to simplify.
you will get
\[ x= \frac{-9± \sqrt{145}}{4} \]
the two roots will be

\[ x= \frac{-9+ \sqrt{145}}{4} \]
and
\[ x= \frac{-9 - \sqrt{145}}{4} \]

using a calculator we will find x = (-9 + 12.0416)/4= 0.7604
and x= (-9 - 12.0416)/4 = -5.26

choice D