How to solve square root equations?

We have removed one square root.

Expand right hand side: 2x−5 = 1 + 2√(x−1) + (x−1)

Simplify: 2x−5 = 2√(x−1) + x

Subtract x from both sides: x−5 = 2√(x−1)

Now do the "square root" thing again:

We have now successfully removed both square roots.

Let us continue on with the solution.

Expand right hand side: x−1 = (x2 − 10x + 25)/4

It is a Quadratic Equation! So let us put it in standard form.

Multiply by 4 to remove division: 4x−4 = x2 − 10x + 25

Bring all to left: 4x − 4 − x2 + 10x − 25 = 0

Combine like terms: −x2 + 14x − 29 = 0

Swap all signs: x2 − 14x + 29 = 0

Using the Quadratic Formula (a=1, b=−14, c=29) gives the solutions:

2.53 and 11.47 (to 2 decimal places)

Let us check the solutions:

2.53: √(2·2.53−5) − √(2.53−1) ≈ −1 Oops! Should be plus 1! 

11.47: √(2·11.47−5) − √(11.47−1) ≈ 1 Yes that one works. 

There is really only one solution:

11.47 (to 2 decimal places)

where is abdul's work? don't see that anywhere posted : /

step-by-step explanation:

2x + 8

step-by-step explanation: