Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

2 x^{2} + 28 x - 550 = 0 2 x^{2} + 28 x - 550 = 0 2 . . . prime number 28 = 2^{2} \cdot 7 550 = 2 \cdot 5^{2} \cdot 11 GCD (2, 28, 550) = 2 = 2 x^{2} + 14 x - 275 = 0 a = 1; b = 14; c = - 275 D = b^{2} - 4 a c = 1 4^{2} - 4 \cdot 1 \cdot (- 275) = 1296 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 4 \pm 1 2 9 6}{2} x_{1, 2} = \frac{- 1 4 \pm 3 6}{2} x_{1, 2} = - 7 \pm 18 x_{1} = 11 x_{2} = - 25 Factored form of the equation: (x - 11) (x + 25) = 0

Solution in text:

2x²+28x-550=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 5184
D > 0 ... The equation has two distinct real roots

x₁ = 11
x₂ = -25

P = {11; -25}