Question

What constant number must be added or subtracted to 4x2+12x+8=0 to solve it by method of completing the square?

Answer 1

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SOLUTION:--


given quadratic equation is 

4x² + 12x +8 = 0

divide each term with 4 

4x² / 4 + 12x /4 + 8 /4 =0

x² + 3x + 2 = 0 

x² +3x = -2

To solve this quadratic equation by completing square method 

x² + 2 × x × 3/2  + ( 3/2 )² - ( 3/2 )² =  -2

we hav to add and subtract  ( 3/2 ) ²

x² + 2 × x × 3/2 + ( 3/2 )² = ( 3/2 )² - 2

⇒ ( x + 3/2 )² = 9 /4 - 2/1

                      = ( 9 - 8 ) /4

                      = 1 / 4

⇒ ( x + 3/2 ) = + or - √ 1 / 4

⇒ x = - 3/2 + or - 1/2

∴ x = - 3/2 + 1/2  or x = -3/2 - 1/2

  x = -2 /2 or x = - 4/2

 x = -1 or x = -2

I hope this is useful to you 

Answer 2

Hi , 

given quadratic equation is 

4x² + 12x +8 = 0

divide each term with 4 

4x² / 4 + 12x /4 + 8 /4 =0

x² + 3x + 2 = 0 

x² +3x = -2

To solve this quadratic equation by completing square method 

x² + 2 × x × 3/2  + ( 3/2 )² - ( 3/2 )² =  -2

we hav to add and subtract  ( 3/2 ) ²

x² + 2 × x × 3/2 + ( 3/2 )² = ( 3/2 )² - 2

⇒ ( x + 3/2 )² = 9 /4 - 2/1

  = ( 9 - 8 ) /4
  = 1 / 4

⇒ ( x + 3/2 ) = + or - √ 1 / 4

⇒ x = - 3/2 + or - 1/2

∴ x = - 3/2 + 1/2  or x = -3/2 - 1/2

  x = -2 /2 or x = - 4/2

 x = -1 or x = -2

I hope this is useful to you .