let the number be x.
a number decreased means
x-
and the sum of the number and 4 is
x+4
to put the expression together, we get. put them in parentheses
x - ( x+4 )
= x - x -4
= - 4
Its shifted down 5 because of the-5 on the end of the first equation
2x - 1 = √(8 - x)
Squaring
(2x - 1)² = 8 - x
4x² - 4x + 1 = 8 - x
4x² - 3x -7 = 0
(4x - 7)(x + 1) = 0
4x = 7 or x = -1
x = 7/4 or x=-1
x=7/4 checks, 2(7/4)-1 = 10/4 = 5/2, √(8-7/4)=√(25/4) = 5/2, good
x=-1 fails, 2(-1) - 1 = -3, can't be a principal square root
Answer: -1 is extraneous
