How do you solve 2x ^ { 2} - 12x + 18= 0?

1 Answer
Apr 30, 2018

The only solution is x=3.

Explanation:

First, divide everything by 2.

2x^2-12x+18=0

x^2-6x+9=0

Then, find two numbers that multiply to 9 (the last number) and add up to -6 (the middle number). These two numbers are -3 and -3. Split the x terms up into these values:

x^2-3x-3x+9=0

Now factor the first two and last two terms separately:

color(red)x(x-3)-3x+9=0

color(red)x(x-3)-color(blue)3(x-3)=0

(color(red)x-color(blue)3)(x-3)=0

(x-3)^2=0

x-3=sqrt0

x-3=0

x=3

That's the only solution. Hope this helped!