Question

(x-2)^2=100
Solve the quadratic function with square roots

Answer 1

It's already nicely set up for you. Find the two square roots and you're gold.

Answer 2

would the answer be 12?

Answer 3

That's one. Where did the other one go?

It helps to write out your process, not just your answer.

Answer 4

theres another one?

Answer 5

Two.

Hint:

(2)^2 = 4
(-2)^2 = 4

Answer 6

if \[x^2=a \Longrightarrow |x|=\sqrt{a}\]

Answer 7

\[\large \sqrt{u^2}=\left| u \right|\]

Answer 8

even power

Answer 9

the reasoning is given by @tkhunny
when you square positive and number
like (-2)^2 (2)^2 the result is the same 4

Answer 10

that is why we are using absolute value

Answer 11

If I squared (x-2) all together and 100, I would get x-2=10 correct?

Answer 12

Well, after all that, did you find the second one?

Here's how you find the first one:

(x-2)^2 = 100

Square Root

x-2 = 10 ==> x = 12

What you did not do was this:

Square Root

x-2 = -10 ==> What?

Answer 13

yes, if you square root something that is squared like root of (x-2)^2, that something can be positive or negative,

\[\sqrt{(x-2)^2} = \left| x-2 \right| = 10\]

Answer 14

solving absolute value probs, that x-2 can be +10 or -10

2 values for x as @tkhunny showed above