Solve Using the Quadratic Formula x^2+7x+6=0

Problem

x2+7*x+6=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=7

c=6

2. State the quadratic formula used to find the roots of the equation.

x=(−b±√(,b2−4*a*c))/(2*a)

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

x=(−7±√(,7−4*(1)*(6)))/(2*(1))

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

x=(−7±√(,49−24))/2

x=(−7±√(,25))/2

5. Evaluate the square root.

x=(−7±5)/2

6. Solve for the two possible values of x by calculating both the addition and subtraction cases.

(x_1)=(−7+5)/2=(−2)/2=−1

(x_2)=(−7−5)/2=(−12)/2=−6

Final Answer

x=−1,−6

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