Question

Use the quadratic formula to solve the following quadratic equation:

x2+2x−8=0

Answer 1

To solve the quadratic equation \( x^2 + 2x - 8 = 0 \) using the quadratic formula, we first identify the coefficients in the standard form \( ax^2 + bx + c = 0 \):

- \( a = 1 \)
- \( b = 2 \)
- \( c = -8 \)

The quadratic formula is given by:

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

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

1. Calculate the discriminant:

\[
b^2 - 4ac = 2^2 - 4(1)(-8) = 4 + 32 = 36
\]

2. Substitute into the quadratic formula:

\[
x = \frac{{-2 \pm \sqrt{36}}}{2 \cdot 1} = \frac{{-2 \pm 6}}{2}
\]

3. Calculate the two possible values for \( x \):

- For the positive root:

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

- For the negative root:

\[
x = \frac{{-2 - 6}}{2} = \frac{-8}{2} = -4
\]

Thus, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are:

\[
x = 2 \quad \text{and} \quad x = -4
\]