Question 65817
<pre><font size = 5><b>Solve for X:
x^2+4x+4=7
The answer I recieved was:
X=.645
My teacher has said this is wrong and is not in
algebra format. Can someone please help me with 
the answer and the correct format? Thank you so 
much for the wonderful help this site brings me 
and many others.

Get 0 on the right by adding -7 to both sides

           x² + 4x + 4 = 7
                    -7  -7
           ---------------
           x² + 4x - 3 = 0

That won't factor, so we use the quadratic formula:
                  ______ 
            -b ± <font face = "symbol">Ö</font>b²-4ac
        x = —————————————
                2a 

where a = 1; b = 4; c = -3

                     _____________ 
             -(4) ± <font face = "symbol">Ö</font>(4)²-4(1)(-3)
        x = ————————————————————————
                     2(1) 
                   _____ 
             -4 ± <font face = "symbol">Ö</font>16+12
        x = —————————————
                 2

                   __ 
             -4 ± <font face = "symbol">Ö</font>28
        x = ——————————
                2

                   ___ 
             -4 ± <font face = "symbol">Ö</font>4·7
        x = ———————————
                2 

                   _
            -4 ± 2<font face = "symbol">Ö</font>7
        x = —————————
                2

                     _
            -4     2<font face = "symbol">Ö</font>7
        x = ——— ± —————
             2      2
                  _
        x = -2 ± <font face = "symbol">Ö</font>7 
                       _
Using the +, x = -2 + <font face = "symbol">Ö</font>7, which
is one solution and equals about .6457513111,
so your answer of .645 is close to that, but rounded 
off to thousandths should be .646, not .645.
                       _ 
Using the -, x = -2 - <font face = "symbol">Ö</font>7, which
is the other solution and equals about -4.645751311

However the solutions that your teacher wants are
                  _
        x = -2 ± <font face = "symbol">Ö</font>7

Edwin </pre>