Question 31046
{{{ sqrt(3x+10) = 1 + sqrt(2x+5) }}} square both sides
{{{ 3x + 10 = (1 + sqrt(2x+5))(1 + sqrt(2x+5)) }}} foil the right side
F: {{{ 1 * 1 = 1 }}}
O: {{{ 1 * sqrt(2x+5) = sqrt(2x+5) }}}
I: {{{ 1 * sqrt(2x+5) = sqrt(2x+5) }}}
L: {{{ sqrt(2x+5)*sqrt(2x+5) = 2x+5 }}} combine like terms
{{{ 3x + 10 = 1 + sqrt(2x+5) + sqrt(2x+5) + 2x + 5 }}}
{{{ 3x + 10 = 6 + 2(sqrt(2x+5)) + 2x }}} Move everything AWAY from the sqrt
{{{ x + 4 = 2(sqrt(2x+5)) }}} divide all parts by 2
{{{ 1x/2 + 2 = sqrt(2x+5) }}} square both sides
{{{ (1/4)x^2 + 2x + 4 = 2x + 5 }}} move everything to the left side
{{{ (1/4)x^2 - 1 = 0 }}} This is the difference of two squares.
{{{ ((1/2)x -1)((1/2)x+1) = 0 }}}
{{{1x/2 -1 = 0 }}} and {{{1x/2 +1 = 0 }}} solve for x in both equations
{{{ 1x/2 = 1 }}} and {{{ 1x/2 = -1 }}}
{{{ x = 2 }}} and {{{ x = -2 }}}