What equation results from completing the square and then factoring?

x^2-10x=46

Move all like term to the same side

x^2-10x-46=0

1. The expression x^2-10x-46 fits into the from ax^2+2b+c, where:

a=1, b=-10 and c=-46

2. Introduce the constant, k, which is 25 in our case

Let k = (b/-2a) ^2

From the earlier step, we know that a=1 and b=-10

Therefore, k = (-10/2*1) ^2 = 25

x^2-10x+25-25-46=0

3. Use square of difference: (a-b) ^2=a^2-2ab+b^2

(x-5) ^2-25-46=0

4. Simplify

(x-5) ^2-71=0

5. Substitute back into the original equation

(x-5) ^2-71=0

6. Add 71 on both sides

(x-5) ^2=71

7. Take the square root of both sides

x-5=plus minus sqrt (71)

8. Add 5 to both sides

x = sqrt (71) + 5 or - sqrt (71) + 5