## anonymous one year ago Use completing the square to solve (x + 7)(x – 9) = 25 for x.

1. SolomonZelman

first expand the product. (x+7)(x-9) = ?

2. anonymous

x^2-9x+7x-63

3. SolomonZelman

yes, (x + 7)(x – 9) = 25 x$$^2$$-9x+7x-63 = 25 add the x's on the left side, x$$^2$$-2x-63 = 25

4. SolomonZelman

Add 63 to both sides, and u then get?

5. anonymous

-38

6. SolomonZelman

x$$^2$$-2x-63 = 25 x$$^2$$-2x-63$$\small\color{red}{+63}$$= 25$$\small\color{red}{+63}$$

7. SolomonZelman

like that, add 63 to both sides. what do you get after doing this?

8. anonymous

ooooooooooh i see. x^2-2x= 88

9. SolomonZelman

yes, and then tell me what number would make the x²-2x +what a perfect square trinomial? (remember the rule DanJS posted: "half of the coefficient on x, then squared")

10. anonymous

1?

11. SolomonZelman

that number that makes the left hand side a perfect square trinomial, this number, you should add to both sides of the equation.

12. SolomonZelman

yes, it is 1.

13. SolomonZelman

So, add 1 to both sides

14. SolomonZelman

x$$^2$$-2x$$\small\color{blue}{+1}$$= 88$$\small\color{blue}{+1}$$

15. SolomonZelman

can you go on from here? steps just in case: $$1.$$ simplify the right side $$2.$$ factor the left side (it should look like " (x-number)² ") $$3.$$ take the square root of both sides (and don't forget the $$\pm$$) $$4.$$ add 1 to both sides of the equation