Question

solve for x , x = 2√x+3​

Answer 1

Answer:

Radical Equation entered :

x-2√x-3 = 0

Step by step solution :

STEP

1

:

Isolate the square root on the left hand side

Original equation

x-2√x-3 = 0

Isolate

-2√x = -x+3+0

Tidy up

2√x = x-3

STEP

2

:

Eliminate the radical on the left hand side

Raise both sides to the second power

(2√x)2 = (x-3)2

After squaring

4x = x2-6x+9

STEP

3

:

Solve the quadratic equation

Rearranged equation

x2 - 10x + 9 = 0

This equation has two rational roots:

{x1, x2}={9, 1}

STEP

4

:

Check that the first solution is correct

Original equation, root isolated, after tidy up

2√x = x-3

Plug in 9 for x

2√(9) = (9)-3

Simplify

2√9 = 6

Solution checks !!

Solution is:

x = 9

STEP

5

:

Check that the second solution is correct

Original equation, root isolated, after tidy up

2√x = x-3

Plug in 1 for x

2√(1) = (1)-3

Simplify

2√1 = -2

Solution does not check

2 ≠ -2

One solution was found :

x = 9