1.) 4s² + 9 =12s ? and this x²-14=5x ?

Question

how can I solve these equations?

Answer 1

Hey there Hailey, let me walk you through it with a problem similar to the ones you have provided:
Solve 2x² - 12 = 10x

 

1. The first thing we need to do is move everything to the left side of the equation:
2x² - 10x - 12 = 0

2. Now we need to factor the left side giving:
(2x + 2)(x - 6) = 0
*If you need help factoring see Nimita's response


3. In order for the left side to equal zero either of the factors need to be zero so solve for each set equal to zero
2x + 2 = 0
2x = -2
x = -1

x - 6 = 0
x = 6

So our answers to this problem are x = -1 or x = 6 (also written as x = -1,6)

4. Finally it's good practice to check the answers in our original equation:
2(-1)² - 12 = 10(-1)
2(1) - 12 = -10
2 - 12 = -10
-10 = -10 (correct)

2(6)² - 12 = 10(6)
2(36) - 12 = 60
72 - 12 = 60
60 = 60 (correct)

To review:

1. Move everything to the left side
2. Factor it
3. Set both equal to zero and solve for the two answers
4. Check the answers

Give it a try with the ones you have and if you get stuck let me know where and I would be happy to help!

Answer 2

Hi Hailey,

 

You solve these equations by doing a "backwards" FOIL method or by factoring. 

 

The first equation: 

4s² + 9 = 12s

4s² - 12s + 9 = 0

(2s - __) (2s - __) = 0

(2s - 3) (2s - 3) = 0

(2s-3)²=0

 

Now just to check, you want to go ahead and do FOIL: 

 

4s² - 6s - 6s +9 = 0

4s² -12s + 9 = 0

 

___________________________________________________

x²-14=5x

 

x² - 5x -14 = 0

(x + __ ) (x - __) = 0

(x + 2) (x - 7) = 0

 

Now just to check, you want to go ahead and do FOIL:

x² -7x +2x -14 = 0

x² -5x - 14 = 0