Question 974369
SQRT(x + 8) + SQRT(x + 15) = SQRT(9x + 40).    This must be squared twice and I'm stuck. 
<pre>Where are you stuck? Why don't you show what you've done so someone can see and tell you why and/or
where you're getting stuck? I got {{{highlight_green(x = 1)}}}
<u>SOLUTION BELOW:</u><pre>{{{sqrt(x + 8) + sqrt(x + 15) = sqrt(9x + 40)}}}
{{{(sqrt(x + 8) + sqrt(x + 15))^2 = (sqrt(9x + 40))^2}}} ------ Squaring both sides
{{{(x + 8) + 2 * sqrt((x + 8)(x + 15)) + x + 15 = 9x + 40}}} 
{{{x + 8 + x + 15 + 2 * sqrt(x^2 + 23x + 120) = 9x + 40}}}
{{{2x + 23 + 2 * sqrt(x^2 + 23x + 120) = 9x + 40}}}
{{{2 * sqrt(x^2 + 23x + 120) = 9x + 40 - 2x - 23}}}
{{{2 * sqrt(x^2 + 23x + 120) = 7x + 17}}}
{{{(2 * sqrt(x^2 + 23x + 120))^2 = (7x + 17)^2}}} ------- Squaring both sides
{{{4(x^2 + 23x + 120) = 49x^2 + 238x + 289}}}
{{{4x^2 + 92x + 480 = 49x^2 + 238x + 289}}}
{{{49x^2 - 4x^2 + 238x - 92x + 289 - 480 = 0}}}
{{{45x^2 + 146x - 191 = 0}}}
{{{45x^2 + 191x - 45x - 191 = 0}}}
{{{x(45x + 191) - 1(45x + 191) = 0}}}
(x – 1)(45x + 191) = 0
{{{highlight_green(x = 1)}}}		OR 		x = {{{- 191/45}}} (ignore)