Question

question
video examples
solve the equation for all real solutions in simplest form.
$k^2 + 5k - 3 = 0$
answer
attempt 1 out of 3
+ additional solution - no solution
$k = $
submit answer

Explanation:

Step1: Identify quadratic coefficients

For $k^2 + 5k - 3 = 0$, $a=1$, $b=5$, $c=-3$

Step2: Apply quadratic formula

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

Step3: Calculate discriminant

$\Delta = 5^2 - 4(1)(-3) = 25 + 12 = 37$

Step4: Substitute into formula

$k=\frac{-5\pm\sqrt{37}}{2(1)}$

Answer:

$k=\frac{-5+\sqrt{37}}{2}$ and $k=\frac{-5-\sqrt{37}}{2}$