Determine the solution set for the following: √6x+x^2 + √x-6 = 0Show solution and explain the process.

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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Supposing that you need to solve the equation `sqrt(6x+x^2)+sqrt(x-6) = 0` , you should move one of the square roots to the right side such that:

`sqrt(6x+x^2) = -sqrt(x-6) `

You need to raise to square to remove the square roots such that:

`6x+x^2 = x-6`

You need to move all terms to the left side such that:

`x^2 + 6x - x + 6 = 0`

`x^2 +5x + 6 = 0`

You need to use quadratic formula such that:

`x_(1,2) = (-5+-sqrt(25-24))/2`

`x_(1,2) = (-5+-1)/2`

`x_1 = -2`

`x_2 = -3`

You need to substitute x = -2 in equation such that:

`sqrt(-12+4) = -sqrt(-2-6) =gt sqrt(-8) = -sqrt(-8)`  impossible!

You need to substitute x = -3 in equation such that:

`sqrt(-18+9) = -sqrt(-3-6)` 

`sqrt(-9) = -sqrt(-9)`  impossible!

Hence, the equation has no solutions.

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