<PRE><B>Question 139847</B>
square root of (x-5) - square root of (2x+7) = -3
:
{{{sqrt(x-5)}}} - {{{sqrt(2x+7)}}} = -3
:
We can arrange this to get rid of the negatives and make it a little easier
{{{sqrt(x-5)}}} + 3 = {{{sqrt(2x+7)}}}
:
Square both sides (FOIL the left side)
[(x-5) + {{{6sqrt(x-5)}}} + 9] = 2x + 7
:
x + {{{6sqrt(x-5)}}} + 9 - 5 = 2x + 7
:
x + {{{6sqrt(x-5)}}} + 4 = 2x + 7
:
We want the radical by itself on the left:
{{{6sqrt(x-5)}}} = 2x -x + 7 - 4
:
{{{6sqrt(x-5)}}} = (x + 3)
:
Square both sides again (FOIL the right side)
36(x-5) = x^2 + 6x + 9
:
36x - 180 = x^2 + 6x + 9
:
combine like terms to obtain a quadratic equation
0 = x^2 + 6x - 36x + 9 + 180
:
x^2 - 30x + 189 = 0
Factor
(x-9)(x-21) = 0
Two solutions
x = 9
x = 21
:
Try both solutions in the original equation to make sure they are both valid


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