<PRE><B>Question 937803</B>
five times the square root of 1 less than a number is equal to 3 more than the number .
 find the number.
:
Write an equation for exctly for what it says
{{{5*sqrt(x-1) = x + 3}}}
square both sides
25(x-1) = (x + 3)^2
FOIL (x+3)(x+3)
25x - 25 = x^2 + 6x + 9
Combine like terms on the right
0 = x^2 + 6x - 25x + 9 + 25
0 = x^2 - 19x + 34
Factors to
(x-17)(x-2) = 0
Two solutions
x = 17
and 
x = 2
:
We must check both solutions in the original equation
{{{5*sqrt(17-1) = 17 + 3}}}
{{{5*sqrt(16) = 20}}}
5*4 = 20; a good solution
and
{{{5*sqrt(2-1) = 2 + 3}}}
{{{5*sqrt(1) = 5}}}
5 * 1 = 5; also a good solution</PRE>