# 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± √52

step 3 Solve the above expression for minus & plus values

x_{1} = 1 + √52

= 1 + 2.2361/2

x_{2} = 1 - √52

= 1 - 2.2361/2

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

x_{1} = 3.2361/2

x_{1} = 1.618

x_{2} = -1.2361/2

x_{2} = -0.618

x_{1} = 1.618 & x_{2} = -0.618 are the roots for equation x^{2} - x - 1 = 0