Question 209756
1+square root(x+7)=square root(3x-2)
{{{1 + sqrt(x+7)}}} = {{{sqrt(3x-2)}}}
Square both sides, (FOIL the left):
{{{1 + 2sqrt(x+7) + (x+7)}}} = {{{3x - 2}}}
:
{{{x + 8 + 2sqrt(x+7)}}} = {{{3x - 2}}}
:
{{{2sqrt(x+7)}}} = {{{3x -x - 2 - 8}}}
:
{{{2sqrt(x+7)}}} = {{{2x - 10}}}
Square both sides again, (FOIL the right side)
4(x + 7) = 4x^2 - 20x - 20x + 100
:
4x + 28 = 4x^2 - 40x + 100
:
0 = 4x^2 - 40x - 4x + 100 - 28
a quadratic equation
4x^2 - 44x + 72 = 0
Simplify divide by 4
x^2 - 11x + 18 = 0
Factor
(x-9)(x-2) = 0
Two solutions
x = 9
x = 2
:
It's important that you test both solutions in the original equation, one may not be valid.
I'll let you do that