Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6
Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1
(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1
Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x
Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2
Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2
Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144
Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0
The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0
Divide both sides by -4:
(x - 9) (x - 4) = 0
Split into two equations:
x - 9 = 0 or x - 4 = 0
Add 9 to both sides:
x = 9 or x - 4 = 0
Add 4 to both sides:
x = 9 or x = 4
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct
The solution is:
Answer: x = 9
Alright, so since anything can be squared, the domain is (-inf, inf)
94.2 in would be your answer
Answer:7500
Step-by-step explanation:
if you divide 15000 and 2 you get 7500.and if you get 7500 you have to multiply to check if its correct so 7500 times 2 equals 15000. So the answer is 7500.
