What is the answer to x^2+(x-1)*sqrt(x-2)=118+3x ?

The answer to x^2+(x-1)*sqrt(x-2)=118+3x is x=11

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x^2+(x-1)*sqrt(x-2)=118+3x

x^{2} + (x - 1) \cdot x - 2 = 118 + 3 x

x = 11

Solution steps

x^{2} + (x - 1) x - 2 = 118 + 3 x

Expand

x^{2} + (x - 1) x - 2 : x^{2} + x - 2 x - x - 2

x^{2} + x - 2 x - x - 2 = 118 + 3 x

Move

x^{2}

to the right side

x - 2 x - x - 2 = 118 + 3 x - x^{2}

Factor

x - 2 x - x - 2 : x - 2 (x - 1)

x - 2 (x - 1) = 118 + 3 x - x^{2}

Square both sides:

x^{3} - 4 x^{2} + 5 x - 2 = x^{4} - 6 x^{3} - 227 x^{2} + 708 x + 13924

x^{3} - 4 x^{2} + 5 x - 2 = x^{4} - 6 x^{3} - 227 x^{2} + 708 x + 13924

Solve

x^{3} - 4 x^{2} + 5 x - 2 = x^{4} - 6 x^{3} - 227 x^{2} + 708 x + 13924 : x = 11, x \approx 14.45025 \dots

x = 11, x \approx 14.45025 \dots

Verify Solutions:

x = 11

True

, x \approx 14.45025 \dots

False

The solution is

x = 11

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

x + 9 + x = 3

x - 10 = - 2

3 x^{2} - 2 = 2 x - 1

x + 3 = 3 x - 1

What is the answer to x^2+(x-1)*sqrt(x-2)=118+3x ?
The answer to x^2+(x-1)*sqrt(x-2)=118+3x is x=11
Solve for x: x^2+(x-1)*sqrt(x-2)=118+3x
The solution is x=11