Unknown Value of "x" in Quadratic Equation x2 + x + 1 = 0
-0.5 + 0.866i & -0.5 - 0.866i are the roots of quadratic equation x2 + x + 1 = 0. Users may replace the input values of this equation x2 + x + 1 = 0 to verify the similar calculations or generate complete work with steps to find what is the unknown or root value of x.
Work with Steps for x2 + 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 x2 + x + 1 = 0 or to solve the worksheet problems.
step 1 Address the input parameters and values
Quadratic Equation : x2 + x + 1 = 0
step 2 Substitute a , b and c values in below formula
x = - b ± √b² - 4ac2a
=-(1) ± √(12 - 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
x1 = -1 + √3 . i2
= -1 + 1.7321i2
x2 = -1 - √3 . i2
= -1 - 1.7321i2
step 4 By simplifying the above expressions for x1 & x2
x1 = -1/2+ 1.7321i/2
x1 = -0.5 + 0.866i
x2 = -1/2- 1.7321i/2
x2 = -0.5 - 0.866i
x1 = -0.5 + 0.866i & x2 = -0.5 - 0.866i are the roots for equation x2 + x + 1 = 0
