<PRE><B>Question 448614</B>
Please help me solve this equation: {{{sqrt(5x+39)=x+3}}}
Square both sides
 {{{(sqrt(5x+39))^2=(x+3)^2}}}
:
FOIL (x+3)(x+3) on the right
5x + 39 = x^2 + 6x + 9
:
Combine like terms on the right
0 = x^2 + 6x - 5x + 9 - 39
:
A quadratic equation
x^2 + x - 30 = 0
:
Factors to
(x+6)(x-5) = 0
:
Two solutions
x = -6
x = +5
:
Check both solution in the original problem
{{{sqrt(5(-6)+39)=-6+3}}}
:
{{{sqrt(-30+39)= -3}}}
:
{{{sqrt(9) = -3}}}
3 does not = -3, x=-6 is not a solution
:
try x=5
{{{sqrt(25+39)=5+3}}}
{{{sqrt(64) = 8}}}: x=5 is a valid solutions</PRE>