Answer:
[tex]x=-14\text{ and } x=0[/tex]
Step-by-step explanation:
We are given:
[tex](x+7)^2-49=0[/tex]
And we want to solve for x.
First, we can add 49 to both sides:
[tex](x+7)^2=49[/tex]
Now, we can take the square root of both sides. Since we are taking an even root, we will need plus-minus. Hence:
[tex]x+7=\pm\sqrt{49}[/tex]
Evaluate:
[tex]x+7=\pm7[/tex]
Subtract 7 from both sides:
[tex]x=-7\pm7[/tex]
So, we have two solutions:
[tex]x=-7+7\text{ and } x=-7-7[/tex]
Evaluate:
[tex]x=0\text{ and } x=-14[/tex]
So, from least to greatest, our solutions are:
[tex]x=-14\text{ and } x=0[/tex]
