gfields444 3 years ago Solve x2 – 4x = 12 by completing the square

1. mathslover

$\large{x^2-4x-12=0}$ right?

2. ProgramGuru

you just add 4 to both sides. that will make it $(x-2)^{2}=16$

3. gfields444

@mathslover yes

4. mathslover

ok so now .. $\large{x^2-4x-12=x^2-4x+4-16=0}$ right?

5. gfields444

Yeah

6. mathslover

now can u write $\large{x^2-4x+4=(x-2)^2}$ ??

7. mathslover

(x)^2 -2(2)(x)+2^2 = a^2-2ab+b^2=(a-b)^2=(x-2)^2

8. gfields444

Stuck

9. mathslover

ok so : (x^2-4x+4) = (x-2)^2 ?

10. gfields444

x^2-4x-12=0 x=-2 x=6? or am I doing it wrong

11. mathslover

I think you are doing it wrong ; : x^2-4x-12 = 0 $\large{x^2-4x+4-16=0}$ $\large{(x-2)^2-16=0}$ $\large{(x-2-4)(x-2+4)=0}$ $\large{(x-6)(x+2)=0}$ hence either x = 6 or x = -2

12. mathslover

always remember that : $\large{(a-b)^2=a^2-2ab+b^2}$ $\large{(a+b)^2=a^2+2ab+b^2}$

13. mathslover

or : $\large{(a\pm b)^2=a^2\pm 2ab +b^2}$

14. gfields444

You're awesome! Thank you so much! The formulas were very helpful :)

15. mathslover

nice to hear .. :) best of luck