Unknown Value of "x" in Quadratic Equation x2 - 2x - 1 = 0
2.4142 & -0.4142 are the roots of quadratic equation x2 - 2x - 1 = 0. Users may replace the input values of this equation x2 - 2x - 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 - 2x - 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 - 2x - 1 = 0 or to solve the worksheet problems.
step 1 Address the input parameters and values
Quadratic Equation : x2 - 2x - 1 = 0
step 2 Substitute a , b and c values in below formula
x = - b ± √b² - 4ac2a
=-(-2) ± √(-22 - 4 (1) (-1))2(1)
=2± √4 - 4 (1)(-1)2
=2± √4 + 42
=2± √82
step 3 Solve the above expression for minus & plus values
x1 = 2 + √82
= 2 + 2.8284/2
x2 = 2 - √82
= 2 - 2.8284/2
step 4 By simplifying the above expressions for x1 & x2
x1 = 4.8284/2
x1 = 2.4142
x2 = -0.8284/2
x2 = -0.4142
x1 = 2.4142 & x2 = -0.4142 are the roots for equation x2 - 2x - 1 = 0
