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