Solve for m.2m2+13m+11=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
Question
Solve for m.2m2+13m+11=0Write each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.
Solution
To solve the quadratic equation 2m^2 + 13m + 11 = 0, we can use the quadratic formula, which is m = [-b ± sqrt(b^2 - 4ac)] / 2a. Here, a = 2, b = 13, and c = 11.
First, calculate the discriminant, which is b^2 - 4ac. Discriminant = (13)^2 - 4211 = 169 - 88 = 81.
Since the discriminant is positive, there are two different real solutions.
Now, substitute a, b, and c into the quadratic formula to find the solutions for m.
m = [-13 ± sqrt(81)] / 2*2 m = [-13 ± 9] / 4
So, the solutions are m = (-13+9)/4 = -1 and m = (-13-9)/4 = -5.5.
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