please help me solve x/4+square root over 2x+15=x problem on quadratic equation

Expert Answers

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You need to solve for x the following equation such that:

`x/(4+sqrt(2x + 15)) = x`

You need to multiply by `(4+sqrt(2x + 15))`  such that:

`x = x(4+sqrt(2x + 15))`

Moving the terms to the left side yields:

`x - x(4+sqrt(2x + 15)) = 0`

Factoring out x yields:

`x(1 - 4 - sqrt(2x+15)) = 0`

`x(-3 -sqrt(2x+15)) = 0 => -x(3+ sqrt(2x+15)) = 0`

You need to consider each factor equal to 0 such that:

`-x = 0 =>x = 0`

`3 + sqrt(2x+15) = 0 => sqrt(2x+15) = -3 `

Notice that `sqrt(2x+15) > 0` , hence the equation `sqrt(2x+15) = -3`  is invalid.

Hence, evaluating the solutions to the given equation yields `x = 0.`

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