How do you solve #x=5+(3x-11)^(1/2)#?

Answer 1

#x=9" or " x=4#

recall: #x^(1/2) = sqrtx#
#color(white)(xxxxxx.xxxxxxxx)x-5 = (3x-11)^(1/2)#
#color(white)(xxxxxxxxxxxxx)(x-5)^2 = sqrt(3x-11)^2" " larr# square
#color(white)(xxxxxxxxx)x^2-10x +25 = 3x -11#
#color(white)(xx)x^2 -10x -3x +25 +11 = 0#
#color(white)(xxxxxxxxx)x^2 -13x +36 =0" "larr# factor
#color(white)(xxxxxxxxx)(x-9)(x-4) = 0#
If # x-9 = 0 " "rarr x = 9# If #x-4 =0 " "rarr x= 4#
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Answer 2

To solve the equation x = 5 + (3x - 11)^(1/2), we can follow these steps:

  1. Start by isolating the square root term on one side of the equation. Subtract 5 from both sides: x - 5 = (3x - 11)^(1/2)

  2. Square both sides of the equation to eliminate the square root: (x - 5)^2 = 3x - 11

  3. Expand the left side of the equation: x^2 - 10x + 25 = 3x - 11

  4. Move all terms to one side of the equation: x^2 - 10x - 3x + 25 + 11 = 0

  5. Combine like terms: x^2 - 13x + 36 = 0

  6. Factor the quadratic equation: (x - 4)(x - 9) = 0

  7. 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.

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Answer 3

To solve the equation (x = 5 + \sqrt{3x - 11}), we can follow these steps:

  1. Start by isolating the square root term on one side of the equation:

    [x - 5 = \sqrt{3x - 11}]

  2. 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]

  3. Rearrange the equation to set it equal to zero:

    [x^2 - 10x + 25 - 3x + 11 = 0]

    [x^2 - 13x + 36 = 0]

  4. Factor the quadratic equation:

    [(x - 9)(x - 4) = 0]

  5. 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).

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Answer from HIX Tutor

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.

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