What is the answer to (x-3)sqrt(x^2-5x+4)=2x-6 ?

The answer to (x-3)sqrt(x^2-5x+4)=2x-6 is x=5,x=0

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(x-3)sqrt(x^2-5x+4)=2x-6

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

x = 5, x = 0

Solution steps

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

Subtract

2 x - 6

from both sides

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

Simplify

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

Factor

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

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

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 3 = 0 or x^{2} - 5 x + 4 - 2 = 0

Solve

x - 3 = 0 : x = 3

Solve

x^{2} - 5 x + 4 - 2 = 0 : x = 5, x = 0

x = 3, x = 5, x = 0

Verify Solutions:

x = 3

False

, x = 5

True

, x = 0

True

The solutions are

x = 5, x = 0

- 10 + 7 p = p

x^{2} + 2 x + x^{2} + 2 x + 10 - 20 = 0

2624 x^{2} + 1240 x + 25600 = 260

x^{- \frac{1}{2}} = \frac{1}{x}

What is the answer to (x-3)sqrt(x^2-5x+4)=2x-6 ?
The answer to (x-3)sqrt(x^2-5x+4)=2x-6 is x=5,x=0
Solve for x: (x-3)sqrt(x^2-5x+4)=2x-6
The solution is x=5,x=0