What are the approximate solutions of 2x2 - 7x = 3, rounded to the nearest hundredth?

No real solutions
x ≈ -0.77 and x ≈ 7.77
x ≈ -0.39 and x ≈ 3.89
x ≈ -3.89 and x ≈ 0.39

Question

What are the approximate solutions of 2x2 - 7x = 3, rounded to the nearest hundredth? 

 No real solutions
 x ≈ -0.77 and x ≈ 7.77
 x ≈ -0.39 and x ≈ 3.89
 x ≈ -3.89 and x ≈ 0.39

anonymous · Answer

@satellite73

anonymous · Answer

@iGreen

igreen · Answer

I think they want you to use the quadratic formula..

anonymous · Answer

tbh i am not sure.... I got this big exam and im a little lost on some of these questions

igreen · Answer

Okay, hold on.

anonymous · Answer

ok, and thank you man!

igreen · Answer

First we re-arrange the equation:

$2x^2 - 7x = 3$

Subtract -3 to both sides:

$2x^2 - 7x - 3 = 0$

Our equation is in the form of $ax^2 + bx = c$

Now we can plug it into the quadratic formula.

Formula: $x =\dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

$a = 2$

$b = -7$

$c = -3$

$x =\dfrac{-(-7) \pm \sqrt{-7^2 - 4(2)(-3)}}{2(2)}$

Simplify:

$x =\dfrac{7\pm \sqrt{-7^2 - 4(2)(-3)}}{4}$

Simplify Exponent:

$x =\dfrac{7\pm \sqrt{49 - 4(2)(-3)}}{4}$

Multiply:

$x =\dfrac{7\pm \sqrt{49 - 8(-3)}}{4}$

Multiply:

$x =\dfrac{7\pm \sqrt{49 + 24}}{4}$

Add:

$x =\dfrac{7\pm \sqrt{73}}{4}$

Now we split it into two equations.

$x =\dfrac{7+ \sqrt{73}}{4}$

and

$x =\dfrac{7- \sqrt{73}}{4}$

--------------------------

$x =\dfrac{7+ \sqrt{73}}{4}$

Simplify the Square Root:

$x =\dfrac{7+ 8.54}{4}$

Add:

$x =\dfrac{15.54}{4}$

Divide:

$x \approx3.89$

--------------------------

$x =\dfrac{7- \sqrt{73}}{4}$

Simplify the Square Root:

$x =\dfrac{7- 8.54}{4}$

Subtract:

$x =\dfrac{-1.54}{4}$

Can you divide that? @SouthernRebel101

anonymous · Answer

am i dividing the last thing? the -1.54 over 4?

anonymous · Answer

@iGreen

anonymous · Answer

i am a little confused lol i divided and got -0.385

igreen · Answer

Yep, that's it, that rounds to -0.39

So:

$x \approx 3.89$

and

$x \approx -0.39$

igreen · Answer

So what's your answer choice gonna be?

anonymous · Answer

oh ok um.. C?

anonymous · Answer

i mean D

anonymous · Answer

wait no it would be C right

igreen · Answer

Yep^^

C is right.

anonymous · Answer

xD i am all over

anonymous · Answer

thank you, ill ask for more help when i need it thanky ou so much

igreen · Answer

$\bf x ≈ -0.39~and~x ≈ 3.89$

igreen · Answer

No problem. Just tag me when you do :P

anonymous · Answer

oh i do have a question ill tagg you