How do you solve #x=5+(3x-11)^(1/2)#?
By signing up, you agree to our Terms of Service and Privacy Policy
To solve the equation x = 5 + (3x - 11)^(1/2), we can follow these steps:
-
Start by isolating the square root term on one side of the equation. Subtract 5 from both sides: x - 5 = (3x - 11)^(1/2)
-
Square both sides of the equation to eliminate the square root: (x - 5)^2 = 3x - 11
-
Expand the left side of the equation: x^2 - 10x + 25 = 3x - 11
-
Move all terms to one side of the equation: x^2 - 10x - 3x + 25 + 11 = 0
-
Combine like terms: x^2 - 13x + 36 = 0
-
Factor the quadratic equation: (x - 4)(x - 9) = 0
-
Set each factor equal to zero and solve for x: x - 4 = 0 --> x = 4 x - 9 = 0 --> x = 9
Therefore, the solutions to the equation x = 5 + (3x - 11)^(1/2) are x = 4 and x = 9.
By signing up, you agree to our Terms of Service and Privacy Policy
To solve the equation (x = 5 + \sqrt{3x - 11}), we can follow these steps:
-
Start by isolating the square root term on one side of the equation:
[x - 5 = \sqrt{3x - 11}]
-
Square both sides of the equation to eliminate the square root:
[(x - 5)^2 = 3x - 11]
Expanding the left side:
[x^2 - 10x + 25 = 3x - 11]
-
Rearrange the equation to set it equal to zero:
[x^2 - 10x + 25 - 3x + 11 = 0]
[x^2 - 13x + 36 = 0]
-
Factor the quadratic equation:
[(x - 9)(x - 4) = 0]
-
Set each factor to zero and solve for (x):
[x - 9 = 0 \Rightarrow x = 9]
[x - 4 = 0 \Rightarrow x = 4]
So, the solutions to the equation are (x = 9) and (x = 4).
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7