You can
put this solution on YOUR website!
Start with the given equation
Subtract
from both sides
Square both sides
FOIL the right side
Get everything but the term
to the left side
Combine like terms on the left side
Square both sides
FOIL the left side
Distribute
Get everything to one side
Factor out a 4
Factor the expression in the parenthesis
So we have an answer of
Check:
Plug in
solution works
You can
put this solution on YOUR website!Isolate the radicals by subtracting one of them from both sides:
= 4 -
Square both sides:
= (4 -
)^2
x + 6 = 16 - 8
+ 2-x
x + 6 = 18 - 8
-x
Isolate the remaining radical:
x + x + 6 - 18 = - 8
2x-12 = - 8
Square both sides again:
= (- 8
)^2
- 48x + 144 = 64(2 - x)
-48x+144 = 128-64x
+16x+16 = 0
+ 4x + 4 = 0
(x + 2)(x + 2) = 0
x + 2 = 0
x = -2 [potentially]
Check for extraneous solutions:
= 4 -
?
= 4 -
?
2 = 4 - 2 ?
2 = 2 ; OK
x = -2 is a valid solution
You can
put this solution on YOUR website!Solve:
First, separate the square roots. Subtract
from both sides.
Next, square both sides.
Simplify so that you have only the radical
(or a multiple thereof) on one side.
Add x to both sides.
Subtract 18 from both sides.
Now square both sides again.
Simplify this so that you have a quadratic equation in standard form.
Add 64x to both sides.
Subtract 128 from both sides.
Factor out a 4 to simplify this.
Now factor the parentheses.
Applying the zero products principle, you get the double root:
Check:
Set x = -2.
Simplify.
(
