Question

question
solve for x:
\\(\sqrt{2x + 66} - 19 = -11\\)
answer attempt 1 out of 10
x =

Explanation:

Step1: Isolate the square root term

Add 19 to both sides of the equation:
$\sqrt{2x + 66} - 19 + 19 = -11 + 19$
$\sqrt{2x + 66} = 8$

Step2: Eliminate the square root

Square both sides of the equation:
$(\sqrt{2x + 66})^2 = 8^2$
$2x + 66 = 64$

Step3: Solve for x

Subtract 66 from both sides:
$2x + 66 - 66 = 64 - 66$
$2x = -2$

Divide both sides by 2:
$\frac{2x}{2} = \frac{-2}{2}$
$x = -1$

We should check the solution in the original equation:
Left - hand side: $\sqrt{2\times(-1)+66}-19=\sqrt{64}-19 = 8 - 19=-11$, which is equal to the right - hand side. So $x = - 1$ is a valid solution.

Answer:

$x=-1$