Question

Solve the quadratic equation by taking the square root of (x+5)^2=16

Answer 1

`~~~~~(x+5)^2 = 16\\\\\implies x+5 = \pm√(16)\\\\\implies x+5 = \pm 4\\\\\implies x =-5 \pm 4\\ \\\implies x = -9~~ \text{or}~~~x=-1`

Answer 2

Hi okay i’m gonna write the explanation i hope you give me a brilliant if you think I’m deserving it thank you

(x-5)2=16


The first step you can take to solve this quadratic is to take the square root of both sides of the equation.

√[(x-5)2]=√(16)

When you take the square root of a term that is square it equals what is inside the parentheses.

So on the left side, you have x-5

On the right side, you are what we call "forcing" the square root. When this happens, you need to put ±. Why? Good question. When you square a negative number it positive; when you square a positive number it is also positive.

The √16 = ±4

So now we have;
x-5=±4

What do you do with that?
You make two separate equations.

x-5=4 and x-5=-4
x=9 x=1


Let's check our answers

x=9

(x-5)2=16
(9-5)2=16
42=16
16=16 it checks

x=1

(x-5)2=16
(1-5)2=16
(-4)2=16
16=16 it also checks


ANSWER: x=9 and x=1