Verified answer

Without parentheses, there are 3 possible interpretation to your equation.

First interpretation, and only correct interpretation using order of operation:

Only 6 is under √

(√6)x - 8 = x

(√6 - 1)x = 8

x = 8/(√6 - 1)

Second interpretation: 6x is under √. This is not a correct interpretation using order of operation, but can be made so by using √(6x)

√(6x) - 8 = x

√(6x) = x + 8

6x = (x + 8)²

6x = x² + 16x + 64

-64 = x² + 10x

x² + 10x + 25 = -64 + 25

(x + 5)² = -39

x + 5 = ± (√39)i

x = -5 ± (√39)i

Third interpretation: 6x-8 is under √. This is not a correct interpretation using order of operation, but can be made so by using √(6x-8)

√(6x-8) = x

6x - 8 = x²

x² - 6x + 8 = 0

(x - 2) (x - 4) = 0

x = 2, x = 4

We check for any extraneous solutions that may have been introduced by squaring:

x = 2 -----> √(6x-8) = √(12-8) = √4 = 2 = x -----> ok

x = 4 -----> √(6x-8) = √(24-8) = √16 = 4 = x -----> ok

Solutions: x = 2, x = 4

Remember: if first interpretation was not what you meant, then use parentheses.

Mαthmφm

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RE:

Solve this radical equation? √6x-8=x ?

√6x-8=x

How would you do this? I'm not sure how since there are two X's on both sides.

6x 8

You first can add 8 to both sides to get:

sqrt(6x) = x+8

Then square both sides to get rid of the radical:

6x = (x+8)^2

Then FOIL out and combine like terms to get:

x^2 + 10x +64 = 0

Not factorable so you need to use the quadratic formula, in which the discriminant shows that the roots are nonreal.

So basically you just need to solve the quadratic formula to get the nonreal roots, as this function never crosses the x axis.

I am not certain if the first x on the left hand side is under the radical sign. But assuming it isn't, rewrite the equation to

x√6 - x = 8

factor out x from left side to get

x (√6 - 1) = 8

Then divide through to isolate x to

get

x = 8/(√6 -1)

Jim

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Square both the sides: 6x-8=x^2 Now, Bring the whole expression to L.H.S: x^2-6x+8=0 Now, The expression is a quadratic expression, all you need is to factorize it: so, x^2-4x-2x+8=0 x(x-4)-2(x-4)=0 (x-4)(x-2)=0 Either x-4=0 ,or, x-2=0. so, x=4 or x=2 ANSWER: x=4,2 i hope this helps :)