Step 2: She did not simplify under the square root correctly
under the square root:
(-6)^2 =36
and -4(5)(-8) =160
therefore under the square root it needs to be square root of 36+160 which is square root of 196.
That answer is 14 when square rooted
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Remember that <span>an extraneous solution of an equation, is the solution that emerges from solving the equation but is not a valid solution.
Lets solve our equation to find out what is the extraneous solution:
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and 
and 
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So, the solutions of our equation are </span> and . Lets replace each solution in our original equation to check if they are valid solutions:
- For
We can conclude that 7 is a valid solution of the equation.
- For
We can conclude that 4 is not a valid solution of the equation; therefore, 4 is a extraneous solution.
We can conclude that the correct answer is: <span>D. the extraneous solution is x = 4</span>
Lets solve our equation to find out what is the extraneous solution:
</span>
<span>
So, the solutions of our equation are </span>
- For
We can conclude that 7 is a valid solution of the equation.
- For
We can conclude that 4 is not a valid solution of the equation; therefore, 4 is a extraneous solution.
We can conclude that the correct answer is: <span>D. the extraneous solution is x = 4</span>