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

1 answer

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.