# Solve for x

• Feb 17th 2010, 04:59 AM
Punch
Solve for x
$
\frac{(2x-14)+12(\sqrt{x+2})}{\sqrt{x+2}}=0
$
• Feb 17th 2010, 05:12 AM
e^(i*pi)
Quote:

Originally Posted by Punch
$
\frac{(2x-14)+12(\sqrt{x+2})}{\sqrt{x+2}}=0
$

From the domain $x > -2$

$(2x-14) + 12\sqrt{x+2} = 0$

$2(x-7) = -12 \sqrt{x+2}$

Cancel out 2 then square:

$x^2-14x+49 = 36x+72$

$x^2-50x-23 = 0$

23 is prime and so solve using quadratic formula

$x = \frac{50 \pm \sqrt{50^2-4 \cdot 1 \cdot -23}}{2}$

$x= 25 \pm 18 \sqrt{2}$

However, if we put these solutions back into the original equation we find that $25 + 18\sqrt{2} \neq 0$ - it is an extraneous root so it should be discarded

$x= 25 - 18 \sqrt{2}$ does equal 0 when put into the original equation so this is a root
• Feb 17th 2010, 05:13 AM
Diagonal
The numerator must be zero, so ignore the denominator, except to see limitations of acceptable values [x NOT<=-2 or it is undefined or complex.]

Divide by 2 to simplify.

Move the radical to one side [watch for sign change] and square both sides.

Give it a try.