Question

Multiply and solve for x: 2x(x – 3) = 5

Answer 1

Do you know how to factor?

Answer 2

no

Answer 3

distribute 2x over (x-3) first
then bring 5 to the other side
you will have a quadratic equation and you know what to do

Answer 4

Right, quadratic formula is one way to go...or just complete the square

\[\large 2x(x - 3) = 5\]
Distribute the 2x into the parenthesis
\[\large 2x^2 - 6x = 5\]
Divide everything by 2
\[\large x^2 - 3x = \frac{5}{2}\]
Take 1/2 the coefficient of the 'x'....square it...and add that to both sides
\[\large x^2 - 3x + \frac{9}{4} = \frac{5}{2} + \frac{9}{4}\]
Complete thesquare on the left
\[\large (x - \frac{3}{2})^2 = \frac{19}{4}\]
square root both sides
\[\large x - \frac{3}{2} = \pm \sqrt{\frac{19}{4}}\]
Finally add \(\large \frac{3}{2}\) to both sides

\[\large x = \pm {\frac{\sqrt{19}}{2}} + \frac{3}{2}\]

which breaks into 2 equations

\(\large x = \frac{\sqrt{19}}{2} + \frac{3}{2}\) and \(\large x = -\frac{\sqrt{19}}{2} + \frac{3}{2}\)

good to know a couple ways to do it