Step-by-step explanation:

Radical Equation entered :

2x-3x = √6x-9x

Step by step solution :

STEP 1.

Isolate the square root on the left hand side

Original equation

2x-3x = √6x-9x

Isolate

-√6x-9x = -2x+3x

Tidy up

√6x-9x = -x

STEP 2

Eliminate the radical on the left hand side

Raise both sides to the second power

(√6x-9x)2 = (-x)2

After squaring

6x-9x = x2

STEP 3

Solve the quadratic equation

Rearranged equation

x2 + 3x = 0

This equation has two rational roots:

{x1, x2}={0, -3}

STEP 4

Check that the first solution is correct

Original equation, root isolated, after tidy up

√6x-9x = -x

Plug in 0 for x

√6•(0)-9•(0) = -(0)

Simplify

√0 = 0

Solution checks !!

Solution is x = 0

STEP 5

Check that the second solution is correct

Original equation, root isolated, after tidy up

√6x-9x = -x

Plug in -3 for x

√6•(-3)-9•(-3) = -(-3)

Simplify

√9 = 3

Solution checks !!

Solution is

x = -3

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Answer:

x= -3 is the answer

Step-by-step explanation:

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