SOLUTION: Solve for x in exact form. (In case the exponents are cut off in the picture, they are 1/2 for 4(x+1), 3/2 for 5(x+1) and 5/2 for (x+1)) {{{ 4(x+1)^(1/2)

SOLUTION: Solve for x in exact form. (In case the exponents are cut off in the picture, they are 1/2 for 4(x+1), 3/2 for 5(x+1) and 5/2 for (x+1)) {{{ 4(x+1)^(1/2) - 5(x+1)^(3/2) + (x+1)^

Question 971615: Solve for x in exact form. (In case the exponents are cut off in the picture, they are 1/2 for 4(x+1), 3/2 for 5(x+1) and 5/2 for (x+1))

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let y = x+1

equation becomes:

4y^.5 -5y^1.5 + y^2.5 = 0

.5 is the same as 1/2
1.5 is the same as 3/2
2.5 is the same as 5/2

rearrange the terms to get:

y^2.5 - 5y^1.5 + y^.5 = 0

factor out a y^.5 to get:

y^.5 * (4y^2 - 5y^1 + y^0) = 0

simplify to get:

y^.5 * (4y^2 - 5y + 4) = 0

factor 4y^2 - 5y + 4 to make it equal to (y-4) * (y-1)

your equation becomes:

y^.5 * (y-4) * (y-1) = 0

set each of these factors equal to 0 to get:

y^.5 = 0
(y-4) = 0
(y-1) = 0

solve for y to get:

y = 0
y = 4
y = 1

replace y with x+1 that you made it equivalent to earlier to get:

x+1 = 0
x+1 = 4
x+1 = 1

solve for x to get:

x = -1
x = 3
x = 0

those are your solutions.

i confirmed they are correct by replacing x in the original equations with those values.

the graph of your original equation is shown below:

it's a pain in the neck to go, but you can also show exponents by using html tags of sup and /sup enclosed by smaller than and greater than signs <>

for example x raise to the 5/2 power would be shown as x(sup)5/2(/sup).

i used () instead of <> to show you how it looks.

use <> and it becomes x^5/2.

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