Solve for x x^2-2x-4=0

Problem

x2−2⁢x−4=0 x squared minus 2 x minus 4 equals 0

Solution

  1. Identify the coefficients of the quadratic equation in the form a⁢x2+b⁢x+c=0 a x squared plus b x plus c equals 0 where a=1 a equals 1 b=−2 b equals negative 2 and c=−4 c equals negative 4

  2. Apply the quadratic formula which is given by x=−b±b2−4⁢a⁢c2⁢a x equals the fraction with numerator negative b plus or minus the square root of b squared minus 4 a c and denominator 2 a

  3. Substitute the values into the formula:

x=−(−2)±(−2)2−4⁢(1)⁢(−4)2⁢(1) x equals the fraction with numerator negative negative 2 plus or minus the square root of open paren negative 2 close paren squared minus 4 times 1 times negative 4 and denominator 2 times 1

  1. Simplify the expression inside the square root (the discriminant):

x=2±4+162 x equals the fraction with numerator 2 plus or minus the square root of 4 plus 16 and denominator 2

x=2±202 x equals the fraction with numerator 2 plus or minus the square root of 20 and denominator 2

  1. Simplify the radical by factoring out the largest square:

x=2±2⁢52 x equals the fraction with numerator 2 plus or minus 2 the square root of 5 and denominator 2

  1. Divide both terms in the numerator by the denominator:

x=1±5 x equals 1 plus or minus the square root of 5

Final Answer

x=1±5 x equals 1 plus or minus the square root of 5

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