Question

Using the quadratic formula find the solution to x^2 - 6x - 16 = 0

Answer 1

To solve the quadratic equation \( x^2 - 6x - 16 = 0 \) using the quadratic formula, we first identify the coefficients from the standard form \( ax^2 + bx + c = 0 \):

- \( a = 1 \)
- \( b = -6 \)
- \( c = -16 \)

The quadratic formula is given by:

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

Now we will substitute the values of \( a \), \( b \), and \( c \) into the formula.

1. Calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = (-6)^2 - 4(1)(-16) = 36 + 64 = 100
\]

2. Now substitute \( b \) and the discriminant into the quadratic formula:

\[
x = \frac{-(-6) \pm \sqrt{100}}{2(1)} = \frac{6 \pm 10}{2}
\]

3. This gives us two possible solutions:

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

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

Thus, the solutions to the equation \( x^2 - 6x - 16 = 0 \) are:

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