Question

Solve the following quadratic equation: x2−6x−20=20
.

Answer 1

To solve the quadratic equation \( x^2 - 6x - 20 = 20 \), we first need to move all terms to one side of the equation. We do this by subtracting 20 from both sides:

\[
x^2 - 6x - 20 - 20 = 0
\]

This simplifies to:

\[
x^2 - 6x - 40 = 0
\]

Next, we can solve this quadratic equation using the quadratic formula, which is given by:

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

Where \( a = 1 \), \( b = -6 \), and \( c = -40 \).

First, we calculate the discriminant \( b^2 - 4ac \):

\[
b^2 - 4ac = (-6)^2 - 4(1)(-40) = 36 + 160 = 196
\]

Now we plug into the quadratic formula:

\[
x = \frac{-(-6) \pm \sqrt{196}}{2(1)} = \frac{6 \pm 14}{2}
\]

Now, we calculate the two possible values for \( x \):

1. For \( x = \frac{6 + 14}{2} \):

\[
x = \frac{20}{2} = 10
\]

2. For \( x = \frac{6 - 14}{2} \):

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

Thus, the solutions to the equation \( x^2 - 6x - 40 = 0 \) are:

\[
x = 10 \quad \text{and} \quad x = -4
\]

Therefore, the final answer is:

\[
\boxed{10} \quad \text{and} \quad \boxed{-4}
\]