Question

Can someone help me solve this??

Answer 1

Refer to the attached image

Answer 2

Answer: No solutions

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Reason:

Subtract 5 from both sides

`\sqrt{\text{x}}+5 = 0\\\\\sqrt{\text{x}}=-5\\\\`

But recall that the range of the parent square root function is the set of nonnegative values. There's no way to have
`\text{y} = \sqrt{\text{x}}` produce a negative number.

Therefore, the equation
`\sqrt{\text{x}}=-5` has no solutions.

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Here's what happens if we squared both sides

`\sqrt{\text{x}}=-5\\\\(\sqrt{\text{x}})^2=(-5)^2\\\\\text{x}=25\\\\`

That's the potential answer, but we need to verify.

`\sqrt{\text{x}}+5 = 0\\\\√(25)+5 = 0\\\\5+5 = 0\\\\10 = 0\\\\`

We get a contradiction, which rules out x = 25 being a possible solution.

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If you are a visual learner, then check out the graph below.

The curve
`\text{y} = \sqrt{\text{x}}+5` never touches the x axis; this means there's no way for it to have a root and it verifies why
`\sqrt{\text{x}}+5 = 0` has no solutions.

I used GeoGebra to make the graph, but Desmos is another useful option.