Solve the quadratic equation. List your solutions. Simply if necessary. x^2−6x+9=−8

Question

I couldn't solve this, please help!

Answer 1

x^2 - 6x + 17 = 0 <--- adds 8 to both sides

quadratic formula says:

x = [ 6 +or- sqrt ( 36 - 4 *17)] / 2

= [ 6 +or- sqrt(36-68)]/2

= [ 6 +or- sqrt(-32)]/2

= [ 6 +or- 4*i*sqrt(2)]/2

= 3 +or- 2*i*sqrt(2)

check:

x^2 = ( 3 + 2*i*sqrt(2))^2 = ( 3 + 2*i*sqrt(2))( 3 + 2*i*sqrt(2)) = 9 + 12*i*sqrt(2) - 8 = 1 + 12*i*sqrt(2)

-6x = -18 - 12*i*sqrt(2)

x^2 - 6x = -17 which cancels the 17 in the equation and the answer checks

the answer in bold above 3 +or- 2*i*sqrt(2) is correct

Answer 2

x² - 6x + 9 = -8

x² - 6x = -17

x² - 6x + 9 = -17 + 9 complete the square

(x - 3)² = -8

x - 3 = ± 2i√2

x = 3 ± 2i√2

Answer 3

First we need to put the quadratic equation in standard form ax²+bx+c=0:

x²-6x+9+8=0

x²-6x+17=0

so a=1, b=-6 and c=17.

The descriminant b²-4ac will tell us about the equation's roots:

If b²-4ac>0, there are two unique real roots.

If b²-4ac=0, there is one real root

If b²-4ac<0, there are no real roots.

So, with this one b²-4ac=(-6)²-4(1)(17)=36-68<0

There are no real roots. This means the parabola y=x²-6x+17 does not cross the x-axis (where any real roots are) nor pass through the origin.