Question

Please help!
It is college algebra

Answer 1

x = 4 2/3

Explanation:

8(x^2 -14/3 *x) = 32

Rearrange:

Rearrange the equation by subtracting or addition what is to the right of the equal sign from both sides of the equation :

We have done the opposite and added as it was subtraction sign:

8x + 16 -14/3 * x = 32 + 14/3

Step 1 :

Equation at the end of step 1 seen here below : 32+14/3 -16

+ 16 * x = 32+14/3 -16

Pulling out like terms : Pull out like factors : ( + ) ( + )

= 8x + 8x =16 +14/3 : Note : AB = BA : property of multiplication.

x = 14/3 x = 4 2/3

or

2 is the square of 8

Two solutions were found :

x = 14/3

x = 4 2/3

Trying to factor as a Difference of Squares :

3.2 Factoring: 8x + 8x = 2 *2 = 4 * 2/3

x = 14/3 x = 4 √2.66

This cannot be done as it is creates a new fraction 2 33/50

We find x = 4 2/3 is the answer.

Answer 2

Answer:
`x = 5 , (-1)/(3)`

Explanation:

`8(^{x^(2)-(14)/(3)x}) = 32`

This could be written in index form as :

`2^(3)( ^{x^(2)-(14)/(3)x})=2^(5)`

By laws of indices , we will equate their power , that is :

`3(x^(2) -(14)/(3)x) = 5`

Expanding , we have :

`3x^(2) -14x=5`

`3x^(2) -14x-5=0`

factorising the Quadratic equation , we have :

`3x^(2) -15x + x -5=0`

`3x(x-5)+1(x-5)=0`

`(x-5)(3x+1) = 0`

Therefore:

`x-5 = 0` or
`3x+1=0`

`x = 5 , (-1)/(3)`