Quadratic Equation Solution

[rhoridge]

I can't get the answer they say is the correct answer.
5x^2+17=20x

5x^2-20x+17=0
A=5
B=-20
C=17

I get 20+/- Radial 400-340/10
20+/- 2 Radical 15/10

Then I a not sure about how/when to simplify etc. They say the answer is 10+/- Radical15/5 but I cant get that.

 

[HallsofIvy]

I can't get the answer they say is the correct answer.
5x^2+17=20x

5x^2-20x+17=0
A=5
B=-20
C=17

I get 20+/- Radial 400-340/10
20+/- 2 Radical 15/10

Then I a not sure about how/when to simplify etc. They say the answer is 10+/- Radical15/5 but I cant get that.

As Denis said, you need parentheses: what you wrote would normally be interpreted as 20+/- [2sqrt(15/10)]
But the point is that 20= 2(10) and 10= 2(5) so this can be written as \(\displaystyle (2(10) +/- 2 sqrt(15))/(2(5))= 2(10+/- sqrt(15))/(2(5)) and we can cancel the "2"s in the numerator and denominator.\)

 

[Ishuda]

I can't get the answer they say is the correct answer.
5x^2+17=20x

5x^2-20x+17=0
A=5
B=-20
C=17

I get 20+/- Radial 400-340/10
20+/- 2 Radical 15/10

Then I a not sure about how/when to simplify etc. They say the answer is 10+/- Radical15/5 but I cant get that.

\(\displaystyle \frac{20 \pm 2 \sqrt{15}}{10} = \frac{20}{10} \pm \frac{2 \sqrt{15}}{10} = \frac{10}{5} \pm \frac {\sqrt{15}}{5}=\frac{10 \pm \sqrt{15}}{5}\)

 

[rhoridge]

\(\displaystyle \frac{20 \pm 2 \sqrt{15}}{10} = \frac{20}{10} \pm \frac{2 \sqrt{15}}{10} = \frac{10}{5} \pm \frac {\sqrt{15}}{5}=\frac{10 \pm \sqrt{15}}{5}\)

Why don't you further reduce the 10/5 to only a 2 on top?

 

[Ishuda]

Why don't you further reduce the 10/5 to only a 2 on top?

You could but then, if you wanted to put both quantities, the resulting 2 and the radical, over a common denominator, you would just have to multiply by 5 again. It is a question of how you want (need) to display the answer:
\(\displaystyle \frac{20 \pm 2 \sqrt{15}}{10} = \frac{20}{10} \pm \frac{2 \sqrt{15}}{10} = \frac{10}{5} \pm \frac {\sqrt{15}}{5} = 2\space \pm \frac{\sqrt{15}}{5} = 2\space \pm \frac{\sqrt{3}}{\sqrt{5}} = \frac{10 \pm \sqrt{15}}{5} \)= ...