Solve Using the Quadratic Formula x^2+8x+5=0

Problem

x2+8*x+5=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=5

2. Apply the quadratic formula to find the values of x

x=(−b±√(,b2−4*a*c))/(2*a)

3. Substitute the values of a b and c into the formula.

x=(−8±√(,8−4*(1)*(5)))/(2*(1))

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

x=(−8±√(,64−20))/2

x=(−8±√(,44))/2

5. Factor the square root by identifying the largest perfect square factor of 44.

x=(−8±√(,4⋅11))/2

x=(−8±2√(,11))/2

6. Divide each term in the numerator by the denominator to find the final simplified roots.

x=−4±√(,11)

Final Answer

x=−4±√(,11)

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