Question

Extract the root: (x + 5)^2 = 10x + 74

explain step by step please

Answer 1

(x + 5)^2 = x^2+10 x+25

now substituting:
x^2+10 x+25 = 10x + 74
x^2+25 = + 74
x^2 = 49
x = +- 7

Answer 2

I like Diogo answer. Summarizing the steps.
1. expand (multiply out) the squared term so (x+5) * (x+5) = X^2 + 10x + 25
2. so now we have x^2+10 x+25 = 10x + 74
3. gather like terms (move similar stuff all to one side): subtract 10x from both sides
4. now we have x^2 + 10x -10x + 25 = 10x -10x +74 or x^2 + 25 = 74
5. now subtract 25 from both sides: x^2 + 25 -25 = 74 - 25
6. leaves you with x^2 = 49
7. take square root so then x = \[\pm\]7