Solve for x in the equation: \$ "x" + \sqrt "x" \$ = 6

Isolate the square root term:

\$\sqrt "x" = 6 - "x"\$

Square both sides to eliminate the square root:

\$(\sqrt "x")^2= (6 - "x")^2\$
\$("x") = (6 - "x")^2\$

Expand the right side:

\$ "x" = 36 - 12"x" + "x"^2\$

Rearrange terms to set the equation to zero:

\$"x"^2 - 13"x" + 36 = 0\$

Factor the quadratic equation:

(x - 4)(x - 9) = 0

Find the solutions from the factors:

x = 4 and x = 9

Check the solutions by substituting them back into the original equation.For x = 4

\$\sqrt4 + 4 = 2 + 4 = 6\$

Check the solutions by substituting them back into the original equation.For x = 9

\$\sqrt9 + 9 = 3 + 9 = 12\$

So, the only solution to the equation is x = 4.

This option suggests that the solution to the equation \$\sqrt"x" + "x" = 6\$ is x = 12. However, when we substitute x = 12 into the original equation, we get \$\sqrt12 + 12\$, which doesn’t equal 6. Therefore, option A is incorrect

12

This option suggests that the solution to the equation \$\sqrt "x" + "x" = 6\$ is x = 8. However, when we substitute x = 8 into the original equation, we get \$\sqrt8 + 8\$, which doesn’t equal 6. Therefore, option B is incorrect

8

This option suggests that the solution to the equation \$\sqrt "x" + "x" = 6\$ is x = 6. However, when we substitute x = 6 into the original equation, we get \$\sqrt 6 + 6\$, which doesn’t equal 6. Therefore, option C is incorrect

6

This option suggests that the solution to the equation \$\sqrt "x" + "x" = 6\$ is x = 4. When we substitute x = 4 into the original equation, we get \$\sqrt 4 + 4\$, which does indeed equal 6. Therefore, option D is correct solution

4

Option

D

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