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