Question 419986
{{{sqrt(x^2+10x) = x+4 }}}
Square both sides:
{{{(sqrt(x^2+10x))^2 = (x+4)^2 }}}
Foil the right sides (x+4)(x+4)
x^2 + 10x = x^2 + 8x + 16
;
combine the x's on the left
x^2 - x^2 + 10x - 8x = 16
2x = 16
x = {{{16/2}}}
x = 8
:
:
Check in original equation
{{{sqrt(8^2+10(8)) = 8+4 }}}
{{{sqrt(64+80) = 12 }}}
{{{sqrt(144) = 12 }}}; confirms our solution of x=8