identify the solutions to the equation x^(2)-5x=24 when you solve by completing the square

Question

a. -6, 16

b. -1.5, 4

c. -3, 8

d. no real solutions

Answer 1

 You factor by Completing square, when

  

   X²  + bx +c ,  there is no integer solution to the equation of  m+n = -b   mn= c

 

  i.e.

 

     X ^{2  +} 7X  +5     like ; m+ n = -7, mn = 5

 

     In which we factor by Completing the Square:

 

       X² + 2 (7X/2 ) + 49/4 = -5 + 49/4

 

        ( X + 7/2) ² - 29/4 =

               

       (  X + 7/2 + (√29)/2 ) ( X + 7/2 - (√29)/2) 

 

 

  

Answer 2

(a ± b)² = a² ± 2ab + b²
~~~~~~~
  x² - 5x = 24   
  x² – 2 • 2.5x + 6.25 = 24 + 6.25
 (x – 2.5)² = 30.25
  x – 2.5 = ± 5.5

  x₁ – 2.5 = - 5.5  
  x₁ = - 5.5 + 2.5 = - 3 

  x₂ – 2.5 = + 5.5  
  x₂ = 5.5 + 2.5 = 8 

Answer 3

X²- 8x + 3x - 24 =0

x(x-8) +3(x-8) = 0

(x+3) (x-8)   = 0

x  = -3, 8

answer c.