Question

solve the quadratic equation.
$x^2 - 3x - 13 = 0$
write one exact solution in each box. you can add or remove boxes. if there are no real solutions, remove all boxes.

Explanation:

Step1: Identify quadratic coefficients

For $x^2 - 3x - 13 = 0$, $a=1$, $b=-3$, $c=-13$

Step2: Apply quadratic formula

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

Step3: Calculate discriminant

$\Delta = (-3)^2 - 4(1)(-13) = 9 + 52 = 61$

Step4: Substitute into formula

$x=\frac{3\pm\sqrt{61}}{2}$

Answer:

$\frac{3+\sqrt{61}}{2}$, $\frac{3-\sqrt{61}}{2}$