Question 47601
{{{sqrt(3x + 10) = 5 - 2x}}}
{{{3x + 10 = 25 - 20x + 4x^2}}}
{{{0 = 4x^2 - 23x + 15}}}
{{{0 = 4x^2 - 3x - 20x + 15}}}
{{{0 = (4x^2 - 3x) + (-20x + 15)}}}
{{{0 = x(4x - 3) - 5(4x - 3)}}}
{{{0 = (x - 5)(4x - 3)}}}
x - 5 = 0
x = 5
and
4x - 3 = 0
4x = 3
x = 3/4
Check:
{{{sqrt(3x + 10) = 5 - 2x}}}
{{{sqrt(15 + 10) = 5 - 10}}}
{{{sqrt(25) = -5}}} Nope
Check:
{{{sqrt(3x + 10) = 5 - 2x}}}
{{{sqrt(9/4 + 10) = 5 - 3/2}}}
{{{sqrt(9/4 + 40/4) = 10/2 - 3/2}}}
{{{sqrt(49/4) = 7/2}}} Correct
{{{graph(600,600,-10,10,-10,10,sqrt(3x+10),5-2x)}}}