Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.

Question

Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.
`Find the smallest value of $x$ such that $x^2 + 10x + 25 = 8$.`

Answer 1

Hello, please consider the following.

`x^2 + 10x + 25 = 8\\\\\text{\bf We can notice that } x^2+10x+25=(x+5)^2 \text{ so}\\\\x^2 + 10x + 25 = (x+5)^2=8\\\\\text{\bf We take the root.}\\\\x+5=\pm√(8)\\\\\text{\bf We subtract 5}\\\\\boxed{x=-5-√(8)} \ \ or \ \ x=-5+√(8)`

In the box, you can find the smallest solution.

Thank you.