Question

What is the solution set of `x^ { 2} - 14x = - 38`?

Answer 1

`x=7+sqrt11` and `7-sqrt11`

Explanation:

Use completing the square :

`x^2-14x+49=-38+49`

Simplify:

`(x-7)^2=11`

Square root both sides. Remember that square rooting will give positive and negative answers:

`x-7=sqrt11` and `-sqrt11`

Add 7 to both sides:

`x=7+sqrt11` and `7-sqrt11`

You can see this graphically as well

graph{x^2-14x+38 [-1.58, 18.42, -4.16, 5.84]}