What is the answer to x^2-8x+sqrt(3x-2)=20+sqrt(3x-2) ?

The answer to x^2-8x+sqrt(3x-2)=20+sqrt(3x-2) is x=10

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x^2-8x+sqrt(3x-2)=20+sqrt(3x-2)

x^{2} - 8 x + 3 x - 2 = 20 + 3 x - 2

x = 10

Solution steps

x^{2} - 8 x + 3 x - 2 = 20 + 3 x - 2

Subtract

20 + 3 x - 2

from both sides

x^{2} - 8 x + 3 x - 2 - (20 + 3 x - 2) = 20 + 3 x - 2 - (20 + 3 x - 2)

Simplify

x^{2} - 8 x - 20 = 0

Factor

x^{2} - 8 x - 20 : (x + 2) (x - 10)

(x + 2) (x - 10) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 2 = 0 or x - 10 = 0

Solve

x + 2 = 0 : x = - 2

Solve

x - 10 = 0 : x = 10

x = - 2, x = 10

Verify Solutions:

x = - 2

False

, x = 10

True

The solution is

x = 10

3 x + 45 + 1 = 7

3 x + 1 + x + 2 = 3

5 x + 39 + 6 = 8

2 x - 2 - 7 - 2 x = 1

What is the answer to x^2-8x+sqrt(3x-2)=20+sqrt(3x-2) ?
The answer to x^2-8x+sqrt(3x-2)=20+sqrt(3x-2) is x=10
Solve for x: x^2-8x+sqrt(3x-2)=20+sqrt(3x-2)
The solution is x=10