How would I find the roots of 
, without using the quadratic formula?
So far I have, , how do I return it to it's factored form?
+118608 $$\\9x^2-6x+1=64\\\\
9x^2-6x-63=0\\\\
3(3x^2-2x-21)=0\\\\
3x^2-2x-21=0\\\\$$
You need 2 numbers that multiply to -3*21=-63 and add to -2
That is really easy.
One has to be neg and the other positive (since they mult to a neg)
The bigger one is the neg one because that add to a neg.
there absolute value is only 2 apart.
So
they are -9 and +7
write -2x as -9x+7x
$$\\3x^2-2x-21=0\\\\
3x^2-9x+7x-21=0\\\\
$now factor in pairs$\\\\
3x(x-3)+7(x-3)=0\\\\
(3x+7)(x-3)=0\\\\
3x+7=0\qquad or \qquad x-3=0\\\\
x=-7/3\quad or \quad x=+3 \quad $ slight correction here - thanks Alan :)$\\\\$$
+118608 $$\\9x^2-6x+1=64\\\\
9x^2-6x-63=0\\\\
3(3x^2-2x-21)=0\\\\
3x^2-2x-21=0\\\\$$
You need 2 numbers that multiply to -3*21=-63 and add to -2
That is really easy.
One has to be neg and the other positive (since they mult to a neg)
The bigger one is the neg one because that add to a neg.
there absolute value is only 2 apart.
So
they are -9 and +7
write -2x as -9x+7x
$$\\3x^2-2x-21=0\\\\
3x^2-9x+7x-21=0\\\\
$now factor in pairs$\\\\
3x(x-3)+7(x-3)=0\\\\
(3x+7)(x-3)=0\\\\
3x+7=0\qquad or \qquad x-3=0\\\\
x=-7/3\quad or \quad x=+3 \quad $ slight correction here - thanks Alan :)$\\\\$$
