Arrange the steps to solve the equation √x+3 - √2x-1= -2

√(x + 3) - √(2x - 1) = -2

The first step is to get one radical on either side of the equation:

√(x + 3) = √(2x - 1) - 2

Now raise both sides to the power of 2 :

(√(x + 3))² = (√(2x - 1) - 2)²

x + 3 = (2x - 1) - 4 √(2x - 1) + 4

Simplify to obtain the final radical term on one side of the equation :

x + 3 = 2x - 1 - 4 √(2x - 1) + 4

x + 3 = 2x + 3 - 4 √(2x - 1)

4 √(2x - 1) = x

Raise both sides to the power of 2 again :

(4 √(2x - 1))² = x²

Simplify to get a quadratic equation :

16 (2x - 1) = x²

x² - 32x + 16 = 0

Factoring this is tricky, so just use the quadratic formula to find the values of x :

x = (32 ± √((-32)² - 4•16)) / 2

x = (32 ± √960) / 2

x = (32 ± √(2⁶•3•5)) / 2

x = (32 ± 2³ √15) / 2

x = 16 ± 4 √15

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