Solve for g. g² + 12g + 11 = 0 Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas. g =

To solve the quadratic equation ( g^2 + 12g + 11 = 0 ), we can use the quadratic formula, which states that for any equation of the form ( ax^2 + bx + c = 0 ), the solutions for ( x ) can be found using:

[

x = frac{-b pm sqrt{b^2 – 4ac}}{2a}

]

In this case, ( a = 1 ), ( b = 12 ), and ( c = 11 ).

1. Calculate the discriminant (( b^2 – 4ac )):

[

b^2 – 4ac = 12^2 – 4 cdot 1 cdot 11 = 144 – 44 = 100

]

2. Now, apply the quadratic formula:

[

g = frac{-12 pm sqrt{100}}{2 cdot 1} = frac{-12 pm 10}{2}

]

3. Calculate the two possible solutions:

– First solution:

[

g = frac{-12 + 10}{2} = frac{-2}{2} = -1

]

– Second solution:

[

g = frac{-12 – 10}{2} = frac{-22}{2} = -11