solve x^2-6x=-10 by completing the square

Question

solve x^2-6x=-10 by completing the square

Answer 1

x^2-6x=-10

 

To complete the square look at the coefficient

of the x term... -6

Take half of that ... -3

Square that and add to both sides... (-3)² = 9

 

x² - 6x + 9 = -10 + 9

x² - 6x + 9 = -1

 

The square formed on the left side is

(x + (-6/2))² = (x-3)²

 

(x-3)² = -1

 

Take square root of both sides

 

x - 3 = ±√(-1)

 

√(-1) is what we call i ..., the imaginary number

 

x - 3 = ±i

 

x = 3 ± i

 

Check:

x² - 6x = -10    for  x = 3+i

 

(3+i)² - 6(3+i) = -10

 

Noting (a+b)² = a² +2ab + b²

           and i² = -1

 

3² + 2(3)(i) + i² - 18 - 6i = -10

9 + 6i -1 -18 - 6i = -10

-10 = -10

 

You can verify the same works with x=3-i

 

 

Answer 2

Add 9 to both sides of equation.

 

x² - 6x + 9 = -10 + 9

(x - 3)² = -1

 

Now you can solve for x.