## Jeans123 3 years ago Solve the quadratic equation by completing the square x^2-12+7=0

1. Jeans123

@cruffo

2. phi

3. cruffo

4. cruffo

Ah ha!! instructions say "completing the square", so I guess we'll completing the square :)

5. cruffo

BTW... was the problem x^2-12x+7=0 (original was missing the x on the 12)

6. Jeans123

oops yes:)

7. cruffo

cool. x^2 -12x + 7 = 0 step 1: move the constant over x^2-12x= -7

8. cruffo

step 2: take half the bx term $$12 \div 2 = 6$$

9. cruffo

step 3: square the number in step # $$6^2 = 36$$

10. cruffo

step 4: add the number from step 3 to both sides: $x^2 + 12x + 36 = -7 + 36$

11. cruffo

so far so good?

12. Jeans123

Yep:)

13. cruffo

$x^2 + 12x + 7 = 0$ $x^2 + 12x = -7$ $x^2 + 12x + 36 = -7+36$ step 5: factor the left-hand side, and simplify the right-hand side: $(x+6)^2 = 29$ Hint - the left-hand side always factors to (x + # from step 2, including the sign, either + or -)^2

14. cruffo

from this point, use the square root property to finish solving for x.

15. Jeans123

x^2+12x+7=0?

16. Jeans123

that is what I started with?

17. cruffo

did you just FOIL (x+6)^2 and subtract 29 to zero out the equation! Yep, that is back to where you started... :)

18. cruffo

"Square Root Property" means take the square root $$\sqrt{\;\;\;}$$ of both sides .

19. cruffo

$\sqrt{(x+6)^2} = \pm \sqrt {29}$

20. Jeans123

Ohh!!!:D

21. cruffo

:)

22. Jeans123

I got x=+- -.6148

23. cruffo

$\sqrt{(x+6)^2} = \pm \sqrt {29}$ humm.. $$\sqrt{29}$$ does not simplify (other than decimal approx) so I'm gonna leave it for now... $x+6 = \pm \sqrt{29}$ subtract 6 from both sides (but not from 29, that's inside the square root) $x = -6 \pm \sqrt{29}$ that gives us two solutions: $x = -6 + \sqrt{29} \approx -0.615$ and $x = -6 - \sqrt{29} \approx -11.385$

24. Jeans123

Thank you sooo much!!!!!:D

25. cruffo

np :)