sqrt of (22-12x) +5 = 2x what is x?

Question

(22-12x)^(1/2) + 5 = 2x
after getting x I substituted it back into x and it doesn't equal.
I got 3/2 and 1/2 for x. Is it wrong or is the answer extraneous?

I subsitute 3/2 and 1/2 back in and it didn't work (see above).

Answer 1

I know why u get wrong!
(22-12x)^(1/2) + 5 = 2x
(22-12x)^(1/2) = 2x - 5

Till here, you are correct.
But, when you square both sides, it may be wrong because
for sqrt, 22-12x > 0
x < 11/6

But in right hand side, 2x -5 = 2(11/6) - 5 = -1.33

This means that 2x-5 is always negative!
If you square up negative value, you will get positive result.
So the answer you get is 3/2 and 1/2

we must do as below:
(22 - 12(1/2))^(1/2) + 5
= (22 - 6)^(1/2) + 5
= 16^(1/2) + 5
= -4 + 5 (negative value after sqrt)
=1 = 2 (1/2) in right hand side

same as
22 - 12(3/2))^(1/2) + 5
= (22 - 18)^(1/2) + 5
= 4^(1/2) + 5
= -2 + 5 (negative value after sqrt)
=3 = 2 (3/2) in right hand side

Answer 2

√ (22-12x) + 5 = 2x
√ (22-12x) = 2x – 5
(22-12x) = (2x – 5)^2
= (2x – 5)* (2x – 5)
= 4x^2 – 20x + 25

22 – 12x = 4x^2 – 20x + 25
4x^2 – (20 + 12)x + (25 – 22) = 0
4x^2 – 8x + 3 = 0
aX^2 + bX + c = 0

By using the quadratic equation, we can solve for x:-

X = [- b ± √ (b^2 – 4ac)] / [2a]
= [- (-8) ± √ ({-8}^2 – 4*4*3)] / [2*4]
= [8 ± √ (64 – 48)] / [8]
= [8 ± √(16)] / [8]
= [8 ± 4] / [8]
= [8 + 4] / [8] or [8 - 4] / [8]
= 1.5 or 0.5

Answer 3

sqrt of (22-12x) +5 = 2x is a False statement, so no solution.

Since you got a false statement, x = 3/2 , and x = 1/2 is an extraneous solution.

Definition of Extraneous Solution

Extraneous solution is a solution of the simplified form of an equation that does not satisfy the original equation.

http://www.highpointsmath.com/sitemap/ExtraneousSolution.html

http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut19_radeq.htm

Answer 4

sqrt of (22-12x) +5 = 2x
sqrt of (22-12x) = 2x - 5
22 - 12x = (2x -5)^2
22 - 12x = (2x)^2 - 2*2x*5 + 5^2
22 - 12x = 4x^2 - 20x + 25
4x^2 - 20x + 25 +12x - 22 = 0
4x^2 - 20x +12x +25 - 22 = 0
4x^2 -8x + 3 = 0
x = -b +/- square root of b^2-4ac/2a
a = 4
b = -8
c = 3
b^2-4ac = (-8)^2 - 4 * 4 * 3
= 64 - 48
= 16
So, x = -(-8) +/- sqrt of 16/2*4
= 8 +/- 4/8
ie, 8 + 4/8 or 8 - 4/8
12/8 or 4/8
3/2 or 1/2
So, the answer is 3/2 or 1/2

Answer 5

22 - 12x + 5 = 2x
27 - 12x = 2x
12x = 27 - 2x
12x + 2x = 27
14x = 27
x = 27/14

Answer 6

BEEN a while since I took intermediate algebra in college.

is this how it goes:

(22-12x) +5 = 2x what is x?
22-12X + 5 = 2X
22-12X+5+12X=2X+ 12X
22-5=14X
17=14X
17/14X=14X/14
17/14X=X

I apologize, but did sqrt mean squirt or squared root of-

if that is the case than my answer is most definitely wrong, i am sure