Respuesta :

bayosanuade

Answer:  [tex]x = 5 , \frac{-1}{3}[/tex]

Step-by-step explanation:

[tex]8(^{x^{2}-\frac{14}{3}x}) = 32[/tex]

This could be written in index form as :

[tex]2^{3}( ^{x^{2}-\frac{14}{3}x})=2^{5}[/tex]

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

[tex]3(x^{2} -\frac{14}{3}x) = 5[/tex]

Expanding , we have :

[tex]3x^{2} -14x=5[/tex]

[tex]3x^{2} -14x-5=0[/tex]

factorising the Quadratic equation , we have :

[tex]3x^{2} -15x + x -5=0[/tex]

[tex]3x(x-5)+1(x-5)=0[/tex]

[tex](x-5)(3x+1) = 0[/tex]

Therefore:

[tex]x-5 = 0[/tex]      or [tex]3x+1=0[/tex]

[tex]x = 5 , \frac{-1}{3}[/tex]

Answer:

x = 4 2/3

Step-by-step 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.

Otras preguntas