What is the solution for x in the given equation? (root)9x+7+ (root)2x=7 A. x = 18 and x = 2 B. x = 18 C. x = 2 D. x = 18 and x = -2

C. x = 2

Step-by-step explanation:

Since you have square roots, you need to separate the square roots and square both sides.

Now that one square root is on each side of the equal sign, we square both sides.

Now we isolate the square root and square both sides again.

Every coefficient is a multiple of 7, so to work with smaller numbers, we divide both sides by 7.

Square both sides.

We need to try to factor the left side.

-2 * (-18) = 36 & -2 + (-18) = -20, so we use -2 and -18.

  or  

Since solving this equation involved the method of squaring both sides, we much check for extraneous solutions by testing our two solutions in the original equation.

Test x = 2:

We have a true equation, so x = 2 is a true solution of the original equation.

Now we test x = 18.

Since 19 = 7 is a false equation, x = 18 is not a true solution of the original equation and is discarded as an extraneous solution.

C. x = 2

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