Solve Using the Quadratic Formula x^2+18x+4=0

Problem

x2+18*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=18

c=4

2. Apply the quadratic formula by substituting the values of a b and c into the formula x=(−b±√(,b2−4*a*c))/(2*a)

x=(−18±√(,18−4*(1)*(4)))/(2*(1))

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

x=(−18±√(,324−16))/2

x=(−18±√(,308))/2

4. Factor the square root by finding the largest perfect square factor of 308

√(,308)=√(,4⋅77)

√(,308)=2√(,77)

5. Substitute the simplified radical back into the equation and divide each term by the denominator.

x=(−18±2√(,77))/2

x=−9±√(,77)

Final Answer

x=−9±√(,77)

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