SOLUTION: Give exact and approximate solutions to three decimal places. {{{(x-2)^2=12}}} What are the exact solutions? x=___ (Type an exact answer, using radicals as needed. Rationaliz

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Question 394798: Give exact and approximate solutions to three decimal places.

What are the exact solutions?
x=___
(Type an exact answer, using radicals as needed. Rationalize all denominators. Express complex numbers in terms of i. Use a comma to separate answers as needed.)
What are the approximate solutions?
x=___
(Use a comma to separate answers as needed. Round to the nearest thousandth as needed.)
Answer by MathLover1(20850) (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=1, b=-4, and c=-8

Negate -4 to get 4

Square -4 to get 16 (note: remember when you square -4, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So the solutions are:

or

the exact solutions are

the approximate solutions