Question

Which are the solutions of x2 = –13x – 4?

0, 13
0, –13
StartFraction 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction 13 + StartRoot 153 EndRoot Over 2 EndFraction
StartFraction negative 13 minus StartRoot 153 EndRoot Over 2 EndFraction comma StartFraction negative 13 + StartRoot 153 EndRoot Over 2 EndFraction

Answer 1

To solve the equation \(x^2 = -13x - 4\), we can first rearrange it into a standard quadratic equation format:

\[
x^2 + 13x + 4 = 0
\]

Now, we can use the quadratic formula to find the solutions, which is given by:

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

In our equation, the coefficients are:
- \(a = 1\)
- \(b = 13\)
- \(c = 4\)

Calculating the discriminant \(b^2 - 4ac\):

\[
b^2 - 4ac = 13^2 - 4 \times 1 \times 4 = 169 - 16 = 153
\]

Now we can plug this into the quadratic formula:

\[
x = \frac{-13 \pm \sqrt{153}}{2 \cdot 1}
\]

This simplifies to:

\[
x = \frac{-13 \pm \sqrt{153}}{2}
\]

Thus, the two solutions are:

\[
x = \frac{-13 - \sqrt{153}}{2} \quad \text{and} \quad x = \frac{-13 + \sqrt{153}}{2}
\]

So the correct answer is:

\[
\frac{-13 - \sqrt{153}}{2}, \frac{-13 + \sqrt{153}}{2}
\]

This matches the last option you provided.