Home / Get Math Help
Complete the Square
Result
(x + 5)^2 + 3
Plot
Geometric figure
parabola
Expanded form
x^2 + 10 x + 28
Alternate form
x (x + 10) + 28
(-i x + sqrt(3) - 5 i) (i x + sqrt(3) + 5 i)
Complex roots
x = -5 - i sqrt(3)
x = -5 + i sqrt(3)
Roots in the complex plane
Polynomial discriminant
Δ = -12
Properties as a real function
R (all real numbers)
{y element R : y>=3}
Derivative
d/dx((x + 5)^2 + 3) = 2 (x + 5)
Indefinite integral
integral(3 + (5 + x)^2) dx = x^3/3 + 5 x^2 + 28 x + constant
Global minimum
min{(x + 5)^2 + 3} = 3 at x = -5