solve the quadratic equation.\n\n$x^{2}-7x - 12 = 0$\n\nwrite one exact solution in each box. you can add or…

Explanation:

Step1: Identify coefficients

For the quadratic equation $x^{2}-7x - 12=0$, we have $a = 1$, $b=-7$, $c=-12$.

Step2: Calculate the discriminant

The discriminant $\Delta=b^{2}-4ac=(-7)^{2}-4\times1\times(-12)=49 + 48=97$.

Step3: Apply the quadratic formula

The quadratic formula is $x=\frac{-b\pm\sqrt{\Delta}}{2a}$. Substituting the values, we get $x=\frac{7\pm\sqrt{97}}{2}$.

Answer:

$x=\frac{7 + \sqrt{97}}{2}$, $x=\frac{7-\sqrt{97}}{2}$