Solve Using the Quadratic Formula x^2+10x+14=0

Problem

x2+10*x+14=0

Solution

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

a=1

b=10

c=14

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

x=(−10±√(,10−4*(1)*(14)))/(2*(1))

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

x=(−10±√(,100−56))/2

x=(−10±√(,44))/2

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

x=(−10±√(,4⋅11))/2

x=(−10±2√(,11))/2

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

x=−5±√(,11)

Final Answer

x=−5±√(,11)

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