Solve algebraically 7x^2/8=2(x-1)

Question

Solve algebraically 7x^2/8=2(x-1)

Answer 1

(7x^2)/8=2(x-1)

(7x^2)/8=2x-2

7x^2=16x-16

7x^2-16x+16=0

use the quadratic equation

 

[16+sqrt(256-448)]/14

[16+sqrt(-192)]/14

[16+sqrt(-64*3)]/14

[16+8sqrt(-3)]/14

(16/14)+(8/14)sqrt(-3)

8/7+(4/7)i sqrt(3)

or [8+4i sqrt(3)]/7

 

Answer 2

Multiply both sides by 8:

(8)* 7x² /8 = (8)* (2)(x-1)

7x² = 16(x-1)


Distribute:
7x² = 16x - 16


Subtract 16x - 16 from both sides:
7x² - 16x +16 = 0


Since b² - 4ac = 256 - 4(7)(16) = -192, there exist no real solutions for this equation.


Using quadratic equation:
-(-16) +/- sqrt(256 - 4(7)(16))
----------------------------------
                   2(7)

16 +/- sqrt(256-448)
-----------------
         14


16 +/- sqrt(-192)
--------------------
            14

No real solutions.


Imaginary solutions would be:
16 +/- 8i sqrt(3)
---------------------
          14

or

8 +/- 4i sqrt(3)
-----------------
            7