Question

What is the positive solution to x2−4x−21=0 ?(1 point)

x= __

Answer 1

To solve the equation \( x^2 - 4x - 21 = 0 \), we can use the quadratic formula:

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

In this equation, \( a = 1 \), \( b = -4 \), and \( c = -21 \).

First, we calculate the discriminant:

\[
b^2 - 4ac = (-4)^2 - 4(1)(-21) = 16 + 84 = 100
\]

Now, substitute this back into the quadratic formula:

\[
x = \frac{-(-4) \pm \sqrt{100}}{2(1)} = \frac{4 \pm 10}{2}
\]

This gives us two possible solutions:

1. \( x = \frac{4 + 10}{2} = \frac{14}{2} = 7 \)
2. \( x = \frac{4 - 10}{2} = \frac{-6}{2} = -3 \)

The positive solution is:

\[
x = 7
\]

So the final answer is:

\( x = 7 \)