Use completing the square to solve the equation. x^2 -10x -4 = 0

Question

I know how to solve using the quadratic formula but I don't know how to set it up by completing the square.

Answer 1

x² - 10x = 4

 

    Take half of -10, square it to get 25, and then add 25 to both sides of the equation.

 

x² - 10x + 25 = 29

 

(x-5)² = 29

 

x - 5 = ±√29

 

       x = 5 ± √29

 

Answer 2

In this case where the coefficient of x^2 is 1 you do this.

Add 4 to both sides

 

x^2-10x=4

 

Divide the coefficient of the x term by 2 to get -5

Then write

(x-5)^2=  _____ +4  where you have to work out what to add to the right side to maintain the equality.

 

If you expand the left side you will get the original x^2-10x but also a +25 term.  You must add this to the right side.

 

(x-5)^2=25+4=29

 

Now you can solve for x.