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

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.
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 expression to solve for the + portion of the ±.
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 expression to solve for the – portion of the ±.
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