Question

try: solve the quadratic $x^{2}+6x - 16 = 0$ by using the quadratic formula.

Explanation:

Step1: Identify coefficients

For $ax^2 + bx + c = 0$, here $a = 1$, $b = 6$, $c = -16$.

Step2: Quadratic formula

Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
Substitute values: $x = \frac{-6 \pm \sqrt{6^2 - 4(1)(-16)}}{2(1)}$

Step3: Calculate discriminant

$6^2 - 4(1)(-16) = 36 + 64 = 100$

Step4: Solve for x

$x = \frac{-6 \pm \sqrt{100}}{2} = \frac{-6 \pm 10}{2}$
First solution: $\frac{-6 + 10}{2} = \frac{4}{2} = 2$
Second solution: $\frac{-6 - 10}{2} = \frac{-16}{2} = -8$

Answer:

$x = 2$ or $x = -8$