Use completing the square to solve the equation x2−12x=−24. First determine the number you must add to both sides of the equation.

Question

Use completing the square to solve the equation x2−12x=−24x2-12x=-24. First determine the number you must add to both sides of the equation. 36;−6±12⎯⎯⎯⎯√36;-6±12 36;6±23⎯⎯√36;6±23 24;6±43⎯⎯√24;6±43 144;6±23⎯⎯√144;6±23

Answer 1

 x²−12x=−24

 

given x² + bx

To complete the square we add (b/2)²

to achieve (x + b/2)²

 

For x² - 12x,    b=-12 ,   (b/2)² = (-6)² = 36

You need to add 36 to both sides to achieve

(x-6)² on the left side.

 

x² - 12x = -24

x² - 12x + 36 = -24 + 36

(x-6)² = 12

Take square root of both sides

x-6 = ±√12

 

x = 6 ± 2√3

Answer 2

Add 36 to both sides of the equation.  This will make the left side a perfect square trinomial.

 

x² - 12x + 36 = -24 + 36

 

(x - 6)² = 12

 

 

Square-root both sides of the equation.

 

x - 6 = ±√12

 

 

Can you finish the rest?