Solve Using the Quadratic Formula x^2-8x-4=0

Problem

x2−8*x−4=0

Solution

1. Identify the coefficients a b and c from the quadratic equation in the form a*x2+b*x+c=0

a=1

b=−8

c=−4

2. Apply the formula for the quadratic equation, which is x=(−b±√(,b2−4*a*c))/(2*a)

x=(−(−8)±√(,(−8)2−4*(1)*(−4)))/(2*(1))

3. Simplify the expression inside the square root (the discriminant).

x=(8±√(,64+16))/2

x=(8±√(,80))/2

4. Simplify the radical by factoring out the largest perfect square from 80

√(,80)=√(,16⋅5)

√(,80)=4√(,5)

5. Substitute the simplified radical back into the equation.

x=(8±4√(,5))/2

6. Divide each term in the numerator by the denominator to find the final values of x

x=4±2√(,5)

Final Answer

x=4±2√(,5)

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