Calculators & Converters

    Unknown Value of "x" in Quadratic Equation x2 - x - 1 = 0

    Quadratic Equation Calculator

    1.618 & -0.618 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 - 4 (1)(-1)2

    =1 + 42

    =52

    step 3 Solve the above expression for minus & plus values
    x1 = 1 + 52

    = 1 + 2.2361/2

    x2 = 1 - 52

    = 1 - 2.2361/2

    step 4 By simplifying the above expressions for x1 & x2
    x1 = 3.2361/2
    x1 = 1.618
    x2 = -1.2361/2
    x2 = -0.618

    x1 = 1.618 & x2 = -0.618 are the roots for equation x2 - x - 1 = 0

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