Question

Solve for x.

10−13x−−−−−−−√=x−4




A x = 2 or x = 3

B x=−6 or x = 1

C no solution

D x=−2 or x=−3

Answer 1

No solution

Explanation:

Did the test and got 100%, dont listen to the other guy.

Answer 2

Option D:
`x=-2` or
`x=-3`

Explanation:

To solve the equation
`√(10-13x) =x-4`

To remove the square root, let us square on both sides of the equation, we get,

`(√(10-13x))^(2) =(x-4)^(2)`

Square root gets cancelled and expanding the term
`(x-4)^(2)` , we get,

`10-13x=x^(2) -8x+16`

Adding 13x to both sides,

`10=x^(2) +5x+16`

Subtracting 10 from both sides, we get,

`0=x^(2) +5x+6`

Solving this equation, we get,

`0=(x+2)(x+3)`

Thus,
`x=-2` or
`x=-3`

Hence, the correct option is D.

A.
`x=2` or
`x=3`

Solving the equation results in
`x=-2` or
`x=-3`

Thus,
`x=2` or
`x=3` cannot be a solution to the equation
`√(10-13x) =x-4`

Thus, Option A is not a correct answer.

B.
`x=-6` or
`x=1`

Solving the equation results in
`x=-2` or
`x=-3`

Thus,
`x=-6` or
`x=1` cannot be a solution to the equation
`√(10-13x) =x-4`

Thus, Option B is not a correct answer.

C. No Solution

Solving the equation results in
`x=-2` or
`x=-3`

Hence, there exits a solution to the equation
`√(10-13x) =x-4`

Thus, Option C is not a correct answer.