$$ \left. \begin{array} { l } { x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a } } \ { a = 1 \quad b = 3 \quad c = - 1 } \end{array} ight. $$

Question

$$ \left. \begin{array} { l } { x = \frac { - b \pm \sqrt { b ^ { 2 } - 4 a c } } { 2 a } } \ { a = 1 \quad b = 3 \quad c = - 1 } \end{array} ight. $$

UpStudy AI · Accepted Answer

1. Dada la fórmula cuadrática:

$$
   x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   $$

2. Se tienen los valores:

$$
   a = 1,\quad b = 3,\quad c = -1
   $$

3. Se sustituye en la fórmula:

$$
   x = \frac{-3 \pm \sqrt{3^2 - 4 \cdot 1 \cdot (-1)}}{2 \cdot 1}
   $$

4. Se calcula el discriminante:

$$
   \Delta = 3^2 - 4 \cdot 1 \cdot (-1) = 9 + 4 = 13
   $$

5. Se escribe la solución:

$$
   x = \frac{-3 \pm \sqrt{13}}{2}
   $$
Las soluciones son $$ x = \frac{-3 + \sqrt{13}}{2} $$ y $$ x = \frac{-3 - \sqrt{13}}{2} $$.

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