SOLUTION: Solve the equation for x: x^2 + 4x + 4 = 7 (x + 2)(x + 2) = 7 (x + 2)^2 = 7 x + 2 = +/- radical 7 x = -2 +/- radical 7 Is this correct?

Question 89386This question is from textbook Beginning Algebra
: Solve the equation for x:
x^2 + 4x + 4 = 7
(x + 2)(x + 2) = 7
(x + 2)^2 = 7
x + 2 = +/- radical 7
x = -2 +/- radical 7
Is this correct? This question is from textbook Beginning Algebra

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Yes it's correct. You can use other methods such as the quadratic formula to verify your answer.

So 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=-3

Square 4 to get 16

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

Notice we get the same answer. So our answer is verified.
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