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 =
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 =
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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