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

The answer to sqrt(2x-1)+1=x(3-x) is x=1,x=2-sqrt(2)

Solve for x: sqrt(2x-1)+1=x(3-x)

The solution is x=1,x=2-sqrt(2)

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2 x - 1 + 1 = x (3 - x)

x = 1, x = 2 - 2

Decimal Notation

x = 1, x = 0.58578 \dots

Solution steps

2 x - 1 + 1 = x (3 - x)

Expand

x (3 - x) : 3 x - x^{2}

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

Remove square roots

2 x - 1 = - 6 x^{3} + x^{4} + 11 x^{2} - 6 x + 1

Solve

2 x - 1 = - 6 x^{3} + x^{4} + 11 x^{2} - 6 x + 1 : x = 1, x = 2 + 2, x = 2 - 2

x = 1, x = 2 + 2, x = 2 - 2

Verify Solutions:

x = 1

True

, x = 2 + 2

False

, x = 2 - 2

True

The solutions are

x = 1, x = 2 - 2

3 x + 1 - 1 = 2 - x

4 x^{2} = x + 1

x + 1 = 9 x - 2

x - 3 = 4

x + 5 - x - 3 = 2

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