Question

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

Answer 1

The 3rd dot and 4th dot, you should select to get the correct answer.

Answer 2

The correct solutions for the equation
`\(x^2 = -13x - 4\)` are
`\((-13 - √(153))/2\) and \((-13 + √(153))/2\).`

To find the solutions of the quadratic equation \(ax^2 + bx + c = 0\), you can use the quadratic formula:

`\[ x = (-b \pm √(b^2 - 4ac))/(2a) \]`

In the given equation \(x^2 = -13x - 4\), the coefficients are \(a = 1\), \(b = 13\), and \(c = 4\). Substituting these values into the quadratic formula, you get:

`\[ x = (-13 \pm √(13^2 - 4(1)(-4)))/(2(1)) \]`

Simplifying further:

`\[ x = (-13 \pm √(169 + 16))/(2) \]`

`\[ x = (-13 \pm √(185))/(2) \]`

Therefore, the solutions are:

`\[ x = (-13 - √(185))/(2) \] and x = (-13 + √(185))/(2) \]`

Simplifying the radicals, you get:

`\[ x = (-13 - √(153))/(2) \] x = (-13 + √(153))/(2) \]`

So, the correct solutions are
`\((-13 - √(153))/2\) and \((-13 + √(153))/2\).`