What is the answer to sqrt(x^2+6x)=x+sqrt(2x) ?

The answer to sqrt(x^2+6x)=x+sqrt(2x) is x=0,x=2

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sqrt(x^2+6x)=x+sqrt(2x)

x^{2} + 6 x = x + 2 x

x = 0, x = 2

Solution steps

x^{2} + 6 x = x + 2 x

Square both sides:

x^{2} + 6 x = x^{2} + 2 2 x x + 2 x

x^{2} + 6 x = x^{2} + 2 2 x x + 2 x

Subtract

x^{2} + 2 2 x x + 2 x

from both sides

x^{2} + 6 x - (x^{2} + 2 2 x x + 2 x) = x^{2} + 2 2 x x + 2 x - (x^{2} + 2 2 x x + 2 x)

Simplify

- 2 2 x x + 4 x = 0

Factor

- 2 2 x x + 4 x : - 2 x (2 x - 2)

- 2 x (2 x - 2) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x = 0 or 2 x - 2 = 0

Solve

2 x - 2 = 0 : x = 2

x = 0, x = 2

Verify Solutions:

x = 0

True

, x = 2

True

The solutions are

x = 0, x = 2

2 v = 3 v - 1

x + 1 = 2

5 x = 10 + 15 x

3 = \frac{x}{5}

6 x + 11 x - 35 = 0

What is the answer to sqrt(x^2+6x)=x+sqrt(2x) ?
The answer to sqrt(x^2+6x)=x+sqrt(2x) is x=0,x=2
Solve for x: sqrt(x^2+6x)=x+sqrt(2x)
The solution is x=0,x=2