Calculadora de ecuación cuadrática
Resolver ecuaciones cuadráticas paso a paso
La calculadora resolverá la ecuación cuadrática paso a paso, ya sea completando el cuadrado o usando la fórmula cuadrática. Encontrará tanto las raíces reales como las imaginarias (complejas).
Calculadora relacionada: Calculadora del discriminante
Solution
Your input: solve the quadratic equation $$$x^{2} - 7 x + 13 = 0$$$ by using quadratic formula.
The standard quadratic equation has the form $$$ax^2+bx+c=0$$$.
In our case, $$$a=1$$$, $$$b=-7$$$, $$$c=13$$$.
Now, find the discriminant using the formula $$$D=b^2-4ac$$$: $$$D=\left(-7\right)^2-4\cdot 1 \cdot 13=-3$$$.
Since the discriminant is negative, there will be two complex roots. This means that the given quadratic equation has no real roots.
Find the roots of the equation using the formulas $$$x_1=\frac{-b-\sqrt{D}}{2a}$$$ and $$$x_2=\frac{-b+\sqrt{D}}{2a}$$$
$$$x_1=\frac{-\left(-7\right)-\sqrt{-3}}{2\cdot 1}=\frac{7}{2} - \frac{\sqrt{3} i}{2}$$$ and $$$x_2=\frac{-\left(-7\right)+\sqrt{-3}}{2\cdot 1}=\frac{7}{2} + \frac{\sqrt{3} i}{2}$$$
Answer: $$$x_1=\frac{7}{2} - \frac{\sqrt{3} i}{2}$$$; $$$x_2=\frac{7}{2} + \frac{\sqrt{3} i}{2}$$$