Step 1 :

Isolate the square root on the left hand side :

Original equation x=1-√5Isolate√5=-x+1

Step 2 :

Eliminate the radical on the left hand side :

Raise both sides to the second power(√5)2=(-x+1)2After squaring 5=x2-2x+1

Step 3 :

Rearranged equationx2-2x-4=0This equation has two actual roots: x1=( 2+sqrt( 20))/ 2=3.2361 x2=( 2-sqrt( 20))/ 2=-1.2361

Step 4 :

Check the the very first solution is exactly :

Original equation, source isolated√5=-x+1Plug in 3.2361 for x√5=-( 3.2361) +1Simplify√5=-2.236Solution walk not inspect 2.236≠-2.236

Step 5 :

Check the the second solution is exactly :

Original equation, root isolated√5=-x+1Plug in -1.2361 for x√5=-(-1.2361) +1Simplify√5=2.236Solution checks !!Solution is: x=-1.2361

One systems was found :

x=-1.2361

You are watching: 1+sqrt(5)/2

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