Step by action solution :

Step 1 :

Isolate the square root on the left hand next :

Original equation x=4-√2Isolate√2=-x+4

Step 2 :

Eliminate the radical ~ above the left hand side :

Raise both sides to the 2nd power(√2)2=(-x+4)2After squaring 2=x2-8x+16

Step 3 :

Solve the quadratic equation :

Rearranged equationx2-8x+14=0This equation has actually two real roots: x1=( 8+sqrt( 8))/ 2=5.4142 x2=( 8-sqrt( 8))/ 2=2.5858

Step 4 :

Check that the very first solution is correct :

Original equation, source isolated√2=-x+4Plug in 5.4142 because that x√2=-( 5.4142) +4Simplify√2=-1.414Solution does not check 1.414≠-1.414

Step 5 :

Check that the 2nd solution is exactly :

Original equation, root isolated√2=-x+4Plug in 2.5858 because that x√2=-( 2.5858) +4Simplify√2=1.414Solution check !!Solution is: x= 2.5858

One solution was uncovered :

x= 2.5858


You are watching: 4*sqrt(2)

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