xsquared - 5/2x-39/16=0

Question

Solve by completing the square

 

Answer 1

remember the basic formula ax^2+bx+c=0 or x²-5/2x-39/16=0

To complete the square you move the c to the side of the equal sign the zero is on x²-5/2x=39/16

Then you add (b/2)² to both sides x² - 5/2x + 25/16= 39/16 + 25/16 or (x - 5/4)² = 64/16

You take the square root of both sides getting x-5/4 = ±8/4

x=8/4+ 5/4 = 13/4 or x = -8/4+5/4 = -3/4 

Answer 2

x² - (5/2)x - 39/16 = 0

 

x² - (5/2)x = 39/16

 

(x - 5/4)² = 39/16 + 25/16

 

(x - 5/4)²  = 64/16 ---> (x - 5/4)² = 4

 

√[(x - 5/4)²] = ±2

 

x - 5/4 = 2, or x - 5/4 = -2

 

so, x = 2 + 5/4         or x = -2 + 5/4

 

so, x = 8/4 + 5/4 ---> x = 13/4

 

or x = -8/4 + 5/4 ---> x = -3/4

 

 

so, x = 13/4 or x = -3/4