Step by step solution :
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=x22x+1
Step 3 :
Solve the quadratic equation :Rearranged equationx22x4=0This equation has two actual roots: x1=( 2+sqrt( 20))/ 2=3.2361 x2=( 2sqrt( 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=1.2361You are watching: 1+sqrt(5)/2
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