Select the statement that best describes the solutions to the equation . x-3=square root 4x+9

Question

 A)Both x=0 and x=10 are extraneous solutions

B) Only x=0 is a valid solution; whereas x=10 is an extraneous solution.

C)Only x=10 is a valid solution; whereas x=0 is an extraneous solution

D) Both x=0 and x=10 are valid solutions

Answer 1

For this problem, it is asking you to solve for your values of x. This one is a little tricky because it will give you a polynomial and you would have to factor in order to find the solutions.

x - 3 = √(4x+9) - you would start off by squaring both sides to get rid of your square root

(x - 3)² = 4x + 9

x² - 6x + 9 = 4x + 9 - next you would move all your terms to one side of the equal sign

-4x -9 -4x -9

x² -10x = 0 -then factor

x(x-10) = 0 -set each term equal to 0 to find your x's

x = 0 and x - 10 = 0

+10 +10

x = 0 and x = 10

The last step would be to plug in your x-values into the original equation to make sure that they give you true statements.

So if you plug in 0:

x - 3 = √(4x+9)

0 - 3 = √(4(0) + 9)

-3 = √13

This statement is false so x = 0 is extraneous.

If you plug in 10:

x - 3 = √(4x+9)

10 - 3 = √4(10) + 9)

7 = √49

7 = 7

This statement is true so x = 10 is a solution.

So the final answer is C.

Answer 2

x - 3 = √(4x + 9)

(x - 3)² = 4x + 9

x² - 6x + 9 = 4x + 9

x² - 10x = 0

x(x - 10) = 0

x = 0 and x - 10 = 0 or x = 10

Try out the answers:

Answer: x = 0

0 - 3 = √(4•0 + 9) does not work so we can through that out

Answer: x = 10

10 - 3 = √(4•10 + 9) works so that is the only answer so answer C is correct