# Unknown Value of "x" in Quadratic Equation x^{2} + x + 1 = 0

## Work with Steps for x^{2} + x + 1 = 0

The below work with steps may helpful for grade school students to understand how to find unknown or root values of x for quadratic equation x^{2} + x + 1 = 0 or to solve the worksheet problems.
step 1 Address the input parameters and values

Quadratic Equation : x^{2} + x + 1 = 0

step 2 Substitute a , b and c values in below formula

x = - b ± √b² - 4ac2a

=-(1) ± √(1^{2} - 4 (1) (1))2(1)

=-1± √1 - 4 (1)(1)2

=-1± √1 - 42

=-1± √3 . i2

step 3 Solve the above expression for minus & plus values

x_{1} = -1 + √3 . i2

= -1 + 1.7321i2

x_{2} = -1 - √3 . i2

= -1 - 1.7321i2

step 4 By simplifying the above expressions for x_{1} & x_{2}

x_{1} = -1/2+ 1.7321i/2

x_{1} = -0.5 + 0.866i

x_{2} = -1/2- 1.7321i/2

x_{2} = -0.5 - 0.866i

x_{1} = -0.5 + 0.866i & x_{2} = -0.5 - 0.866i are the roots for equation x^{2} + x + 1 = 0