The solutions are { -1,-11}
Lets solve the given equation:
x^2 + 11x + 121/4 = 125/4
Subtracting 125/4 from both sides:
=>x^2 + 11x + 121/4-125/4= 125/4 -125/4
=> x^2 + 11x - (-4/4) = 0
=> x^2 +11x -(-1) = 0
=>x^2 + 11 x + 1 = 0
This is a quadratic equation so we will use the determinant (b^2-4ac)
a = 1
b = 11
c = 1
b^2-4ac = 11^2-4*1*1 = 117
So this equation has two solutions:
x = (-b -/+ √(b^2-4ac) ) / 2a
x = (-11 -/+ √(117) ) / 2
x = (-11 -/+ 3√(13))/ 2
x = -0.91 or x = -10.9
x = -1 or x = -11 ( rounding off)
hence the solutions are { -1,-11}.
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