Question

solve using the quadratic formula. find exact solutions. leave i in answer. 3x^2-10x+5=0

Answer 1

Do you know the quadratic formula?

Answer 2

You need to use the quadratic formula with a = 3, b = -10, and c = 5.
Then simplify.

Answer 3

yes, I did that, but I got stuck at \[10\pm \sqrt{40}/6\]

Answer 4

\[\large 3x^2+10x +5=0\]\[\large \color{green}{3}x^2+10x +\color{green}5=0\]\[\large x^2 +10x +15 = 0\]\[\large (x^2 +10x) +15=0\]\[\large (x^2 +10x +25) +15 -25 =0\]\[\large (x+5)^2 -10 = 0\]\[\large (x+5)^2 = 10\]\[\large \sqrt{(x+5)^2} =\pm\sqrt{10}\]\[\large x+5 = \pm 10\]\[\large x= -5 \pm \sqrt{10}\]

Answer 5

Here's the quadratic formula:

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

Now we use a = 3, b = -10, and c = 5

\(x = \dfrac{-(-10) \pm \sqrt{(-10)^2 - 4(3)(5)}}{2(3)} \)

\(x = \dfrac{10 \pm \sqrt{100 - 60}}{6} \)

\(x = \dfrac{10 \pm \sqrt{40}}{6} \)

@hannahbanana14 You are up to here, and you are correct so far. Now we simplify the root and then reduce the fraction:

\(x = \dfrac{10 \pm \sqrt{4 \times 10}}{6} \)

\(x = \dfrac{10 \pm \sqrt{4} \sqrt{10}}{6} \)

\(x = \dfrac{10 \pm 2 \sqrt{10}}{6} \)

\(x = \dfrac{5 \pm \sqrt{10}}{3} \)

\(x = \dfrac{5}{3} \pm \dfrac{\sqrt{10}}{3} \)

Answer 6

@Jhannybean
1) the problem specifically asks for the quadratic formula, not completing the square.
2) if you are using the complete the square method, since the leading coefficient was 3, not 1, you need to divide both sides of the equation by 3. You divided the x^2 term by 3 and multiplied the constant by 3, which gave you a different equation to solve. That's why your answer is incorrect.

Answer 7

i don't understand where the i is supposed to come in... or does it not need it

Answer 8

There is no i. The answer is real.

Answer 9

ok that's what i thought

Answer 10

thanks so much!

Answer 11

Ahh... i messed up then.