Solve the following equation \$ 2 + \sqrt(8 + 2x) = 2\$.

Given equation

\$ 2 + \sqrt(8 + 2x) = 2\$

Subtract 2 from both sides of the equation:

\$2 + \sqrt(8 + 2x) - 2 = 2 - 2\$

\$\sqrt(8 + 2x) = 0\$

Eliminate the Square Root by Squaring Both Sides:

\$\sqrt(8 + 2x)^2 = 0^2\$

8 + 2x = 0

Subtract 8 from both sides and Divide both sides by 2:

2x = - 8

x = - 4

Substitute x = − 4 back into the original equation to check

\$2 + \sqrt(8 + 2(-4)) = 2\$

Simplify inside the square root:

\$(2 + \sqrt(8 - 8)) = 2\$

2 = 2

Since the left side equals the right side, the solution x = − 4 is correct.

-4 is correct because substituting -4 into \$2 + \sqrt(8 + 2x) = 2\$ results \$2 + \sqrt(8 + 2(-4)) = 2\$, which simplifies to 2 + 0 = 2

-4

-6 is not a solution because substituting -6 into \$2 + \sqrt(8 + 2x) = 2\$ results \$2 + \sqrt(8 + 2(-6)) = 2\$, which simplifies to \$2 + \sqrt(-4) = 2\$, and is not a real number

-6

12 is not a solution because substituting 12 into \$2 + \sqrt(8 + 2x) = 2\$ results \$2 + \sqrt(8 + 2(12)) = 2\$, which simplifies to \$2 + \sqrt(32) ne 2\$

12

-25 is not a solution because substituting -25 into \$2 + \sqrt(8 + 2x) = 2\$ results \$2 + \sqrt(8 + 2(-25)) = 2\$, which simplifies to \$2 + \sqrt(-42) = 2\$, and is not a real number

-25

Option

A

Can you summarize what you’ve understood in the above steps?