Question

llowing equation for x. enter multiple answers separated by a comma and if there are no solutions. \\(\sqrt{4x + 6} + 2 = 6\\)

Explanation:

Step1: Isolate the square root term

Subtract 2 from both sides.
$\sqrt{4x+6} = 6 - 2$
$\sqrt{4x+6} = 4$

Step2: Eliminate the square root

Square both sides of the equation.
$(\sqrt{4x+6})^2 = 4^2$
$4x + 6 = 16$

Step3: Solve for x

Subtract 6, then divide by 4.
$4x = 16 - 6$
$4x = 10$
$x = \frac{10}{4} = \frac{5}{2}$

Step4: Verify the solution

Substitute $x=\frac{5}{2}$ into original equation.
$\sqrt{4\times\frac{5}{2}+6}+2 = \sqrt{10+6}+2 = \sqrt{16}+2 = 4+2=6$, which matches the right-hand side.

Answer:

$\frac{5}{2}$