What is the answer to (3+sqrt(5x-6))^2=(2x)^2 ?

The answer to (3+sqrt(5x-6))^2=(2x)^2 is x=3

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(3+sqrt(5x-6))^2=(2x)^2

(3 + 5 x - 6)^{2} = (2 x)^{2}

x = 3

Solution steps

(3 + 5 x - 6)^{2} = (2 x)^{2}

Move

(2 x)^{2}

to the left side

(3 + 5 x - 6)^{2} - 4 x^{2} = 0

Factor

(3 + 5 x - 6)^{2} - 4 x^{2} : (3 + 5 x - 6 + 2 x) (3 + 5 x - 6 - 2 x)

(3 + 5 x - 6 + 2 x) (3 + 5 x - 6 - 2 x) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 + 5 x - 6 + 2 x = 0 or 3 + 5 x - 6 - 2 x = 0

Solve

3 + 5 x - 6 + 2 x = 0 :

No Solution for

x \in R

Solve

3 + 5 x - 6 - 2 x = 0 : x = 3

x = 3

Verify Solutions:

x = 3

True

The solution is

x = 3

x + 7 = 7^{2}

5 - 5 - x = x

38 - 8 x^{3} + 71 = 0

x - 3 = x

x - 6 = x + 6

What is the answer to (3+sqrt(5x-6))^2=(2x)^2 ?
The answer to (3+sqrt(5x-6))^2=(2x)^2 is x=3
Solve for x: (3+sqrt(5x-6))^2=(2x)^2
The solution is x=3