How do you solve this problem? 9-(x-5)^3/4 = 18?

Question

Note: The portion stated as 3/4 is a exponent as a fraction

Answer 1

9-(x-5)^3/4 = 18

-(x-5)^3/4 = 9

(x-5)^3/4 = -9

x -5 = (-9)^4/3

x - 5 = 18.72... Sorry to disagree with mrgets but I can't see why this could be negative

x = 23.72....

Substituting this back in does work if you remember that 18.72...^(3/4) can be ± 9

Just a further thought looking at the other answers but x must be ≥ 5 otherwise you cannot find a real x that fits (x - 5)^(3/4) as the fourth root of negative numbers is complex.

Answer 2

Quite Easy

9 - ( x - 5) ^ 3/4 = 18. (Given)

- (x -5)^ 3/4 = 18 - 9 = 9

(x -5) ^ 3/4 = -9

(x - 5 ) * (x - 5) * (x -5) divided by (x - 5)* (x -5) * (x -5) * (x - 5)

= - 9 [As per theory of indices : (x ^ m/n) = (x ^ m) / (x ^ n) ]

By cancelling the common (x - 5) in both the Numerator & the Denominator, we get

1 / (x -5) = -9

(x - 5) = - 1/9

x = 5 - 1/9

x = 44 / 9 or 4 and 8/9 ANSWER

Answer 3

9 - (x - 5)^(3 / 4) = 18
9 - fourth root (x - 5)^3 = 18
- fourth root (x-5)^3 = 9
Sine what's under the radical sign must always be positive (when talking about even roots such as 2 and 4), and if it is positive that means that you will have a negative number equal 9 (which obviously is not true), there are no REAL solutions. Now, if you are looking for imaginary (containing i) solutions, then it is not as simple. Hope this helped a little.

Answer 4

Hello,

Subtract 9 from both sides and we have -(x-5)^(3/4) = 9 divide both sides by -1 giving us (x-5)^(3/4) = -9

So taking both sides to the (4/3) power gives us

x-5 = (-9)^(4/3) or x-5 = 18.721 or -18.721 then x = 18.721 + 5 =23.721 or using x - 5 = -18.721 we have x = -13.721.

Checking ;

If we use 23.721 we get 9-9 =0 this one doesn't check.

Now using -13.721 we have 9 -(-9) = 18


Hope This Helps.



-13.721

Answer 5

Minus 9 from both sides to get: -(x-5)^3/4=9

Multiply both by -1 to get: (x-5)^3/4=-9

You can take the root of 4/3 from both sides (cancelling the right side out): x-5=-9^4/3

Move the negative back to the other side: -x +5 =9^4/3

Get your number for 9^4/3

Minus 5 from it

Move your negative back over.

Sorry...don't have a calculator.

Answer 6

You can not answer this question in the real domain. The answer is a complex number using i. In the real domain you can not take the square root of a negative number, nor the fourth root.

Answer 7

-(x-5)^3/4=18-9
-(x-5) = 9^4/3
5-x=18.72
-x=13.72
x=-13.72