Question

x=-1+square root 5
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Answer 1

Answer:

x = -1.2361

Step-by-step explanation:

Radical Equation entered :

x = 1-√5

Step by step solution :

STEP

1

:

Isolate the square root on the left hand side

Original equation

x = 1-√5

Isolate

√5 = -x+1

STEP

2

:

Eliminate the radical on the left hand side

Raise both sides to the second power

(√5)2 = (-x+1)2

After squaring

5 = x2-2x+1

STEP

3

:

Solve the quadratic equation

Rearranged equation

x2 - 2x -4 = 0

This equation has two real roots:

x1 = ( 2 + sqrt( 20) ) / 2 = 3.2361

x2 = ( 2 - sqrt( 20) ) / 2 = -1.2361

STEP

4

:

Check that the first solution is correct

Original equation, root isolated

√5 = -x+1

Plug in 3.2361 for x

√5 = -( 3.2361) +1

Simplify

√5 = -2.236

Solution does not check

2.236 ≠ -2.236

STEP

5

:

Check that the second solution is correct

Original equation, root isolated

√5 = -x+1

Plug in -1.2361 for x

√5 = -(-1.2361) +1

Simplify

√5 = 2.236

Solution checks !!

Solution is:

x = -1.2361

i hope it's helpful