Question

PLEASE HELP. I WILL MEDAL AND FAN.
Solve the quadratic equation by completing the square
-3x^2+9x=1

a. 3/2±√6/6
b. -3±√69/3
c. 3±√-3/3
d. 3/2±√69/6

Answer 1

1. Factor by Grouping. 2. Complete the Square. 4. 3. Use the Quadratic. 4 ... irst set of parentheses,place each term to the first power: 9x 1 .

Answer 2

-3x^2 + 9x = 1
divide throughout by -3:
x^2 - 3x = -1/3
Add (b/2)^2 to both sides. b = -3, (b/2)^2 = (-3/2)^2 = 9/4:
x^2 - 3x + 9/4 = -1/3 + 9/4
(x - 3/2)^2 = -4/12 + 27/12 = (27-4)/12 = 23/12
finish the rest of the steps...

Answer 3

sorry, could you walk me through it?

Answer 4

\[
-3x^2 + 9x = 1 \\
\text{Divide throughout by -3:}\\
x^2 - 3x = -\frac 13 \\
\text{To complete the square, add } \left(\frac b2\right )^2 \text{ to both sides:}\\
b = -3,~~ \left(\frac b2\right )^2 = \left(\frac {-3}{2}\right )^2 = \frac 94 \\
x^2 - 3x + \frac 94 = -\frac 13 + \frac 94 \\
(x - \frac 32)^2 = -\frac {4}{12} + \frac {27}{12} = \frac {27-4}{12} = \frac{23}{12}\\
\text{Take square root on both sides:} \\
x - \frac 32 = \pm \sqrt{\frac {23}{12}} \\
x = \frac 32 \pm \sqrt{\frac {23}{12}} \\
\]Can you simplify the right hand side?

Answer 5

so the answer would be a. x=3/2±√6/6 ?

Answer 6

lol i don't know how you could simplify the equation any further….

Answer 7

for sure it's either a. or d.

Answer 8

The right hand side has a radical in the denominator. So you have to rationalize the denominator.
\[
x = \frac 32 \pm \sqrt{\frac {23}{12}} \\
x = \frac 32 \pm \sqrt{\frac {23*3}{12*3}} =
\frac 32 \pm \frac{\sqrt{69}}{6}
\]

Answer 9

oh okay. thank you so much!