Q. \(x^2+6x-16=0\)

We want to solve the quadratic equation

\[
x^{2}+6x-16=0
\]

Step 1: Identify the values of \(a\), \(b\), and \(c\).

A quadratic equation in standard form looks like

\[
ax^{2}+bx+c=0
\]

Here:

• \(a=1\)
• \(b=6\)
• \(c=-16\)

Step 2: Use the quadratic formula.

The quadratic formula is

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

Substitute \(a=1\), \(b=6\), and \(c=-16\):

\[
x=\frac{-6\pm\sqrt{6^{2}-4\cdot 1\cdot (-16)}}{2\cdot 1}
\]

Step 3: Simplify inside the square root (the discriminant).

First compute \(6^{2}\):

\[
6^{2}=36
\]

Now compute \(-4ac\):

\[
-4\cdot 1\cdot (-16)=64
\]

So the discriminant is:

\[
b^{2}-4ac=36+64=100
\]

Step 4: Take the square root.

\[
\sqrt{100}=10
\]

Step 5: Substitute back into the quadratic formula.

\[
x=\frac{-6\pm 10}{2}
\]

Step 6: Split into two solutions.

First solution using \(+\):

\[
x=\frac{-6+10}{2}=\frac{4}{2}=2
\]

Second solution using \(-\):

\[
x=\frac{-6-10}{2}=\frac{-16}{2}=-8
\]

Final Answer:

\[
x=2 \quad \text{or} \quad x=-8
\]