Solve sqrt (x+ a) = x −7 when a=-1

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SUMMARY

The equation sqrt(x + a) = x - 7, with a set to -1, leads to the potential solutions {5}, {10}, and {5, 10}. However, upon substituting x = 5 into the equation, the left side evaluates to 2, while the right side evaluates to -2, indicating that x = 5 is not a valid solution. Therefore, the only valid solution is x = 10, as it satisfies the equation when substituted. The conclusion is that the solution set is {10}.

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rebo1984
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Hi,

If a = -1, what is the solution set of the equation sqrt (x+ a) = x −7

{5}
{10}
{5, 10}
No solution(5,10) correct?

Thanks
 
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rebo1984 said:
Hi,

If a = -1, what is the solution set of the equation sqrt (x+ a) = x −7

{5}
{10}
{5, 10}
No solution(5,10) correct?

Thanks

What do you get when you substitute each potential solution into the original equation?
 
MarkFL said:
What do you get when you substitute each potential solution into the original equation?

It works out.
 
rebo1984 said:
It works out.

Let's try \(x=5\):

$$\sqrt{5-1}=5-7$$

$$2=-2$$

Is this true?
 
rebo1984 said:
It works out.
What "works out"? Which answer did you get?
 

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