x2+x+1=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=1, and c=1 into the quadratic formula and solve for x.

-1±12-4⋅(1⋅1)2⋅1

Simplify the numerator.

One to any power is one.

x=-1±1-4⋅(1⋅1)2⋅1

Multiply 1 by 1.

x=-1±1-4⋅12⋅1

Multiply -4 by 1.

x=-1±1-42⋅1

Subtract 4 from 1.

x=-1±-32⋅1

Rewrite -3 as -1(3).

x=-1±-1⋅32⋅1

Rewrite -1(3) as -1⋅3.

x=-1±-1⋅32⋅1

Rewrite -1 as i.

x=-1±i32⋅1

x=-1±i32⋅1

Multiply 2 by 1.

x=-1±i32

x=-1±i32

Simplify the numerator.

One to any power is one.

x=-1±1-4⋅(1⋅1)2⋅1

Multiply 1 by 1.

x=-1±1-4⋅12⋅1

Multiply -4 by 1.

x=-1±1-42⋅1

Subtract 4 from 1.

x=-1±-32⋅1

Rewrite -3 as -1(3).

x=-1±-1⋅32⋅1

Rewrite -1(3) as -1⋅3.

x=-1±-1⋅32⋅1

Rewrite -1 as i.

x=-1±i32⋅1

x=-1±i32⋅1

Multiply 2 by 1.

x=-1±i32

Change the ± to +.

x=-1+i32

Rewrite -1 as -1(1).

x=-1⋅1+i32

Factor -1 out of i3.

x=-1⋅1-(-i3)2

Factor -1 out of -1(1)-(-i3).

x=-1(1-i3)2

Move the negative in front of the fraction.

x=-1-i32

x=-1-i32

Simplify the numerator.

One to any power is one.

x=-1±1-4⋅(1⋅1)2⋅1

Multiply 1 by 1.

x=-1±1-4⋅12⋅1

Multiply -4 by 1.

x=-1±1-42⋅1

Subtract 4 from 1.

x=-1±-32⋅1

Rewrite -3 as -1(3).

x=-1±-1⋅32⋅1

Rewrite -1(3) as -1⋅3.

x=-1±-1⋅32⋅1

Rewrite -1 as i.

x=-1±i32⋅1

x=-1±i32⋅1

Multiply 2 by 1.

x=-1±i32

Change the ± to -.

x=-1-i32

Rewrite -1 as -1(1).

x=-1⋅1-i32

Factor -1 out of -i3.

x=-1⋅1-(i3)2

Factor -1 out of -1(1)-(i3).

x=-1(1+i3)2

Move the negative in front of the fraction.

x=-1+i32

x=-1+i32

The final answer is the combination of both solutions.

x=-1-i32,-1+i32

Solve Using the Square Root Property x^2+x+1=0