Question

Which are solutions of x2=-11+4?

Answer 1

`x = - √( 7)i \: \: or \: \: x = + √( 7)i`

Step-by-step explanation

The given expression is

`{x}^(2) = - 11 + 4`

Simplify the left hand side to get:

`{x}^(2) = - 7`

Take square root

`x = \pm √( - 7)`

`x = \pm √( 7) * √( - 1)`

Note that:

`{i}^(2) = - 1 \implies √( - 1) = i`

`x = \pm √( 7)i`

Split the plus or minus sign

`x = - √( 7)i \: \: or \: \: x = + √( 7)i`

Answer 2

For this case we have a quadratic equation of the form:

`ax ^ 2 + bx + c = 0\\x ^ 2 + 11x-4 = 0`

Where:

`a = 1\\b = 11\\c = -4`

We find the roots:

`x = \frac {-b \pm \sqrt {b ^ 2-4 (a) (c)}} {2 (a)}\\x = \frac {-11 \pm \sqrt {11 ^ 2-4 (1) (- 4)}} {2 (1)}\\x = \frac {-11 \pm \sqrt {121 + 16}} {2}\\x = \frac {-11 \pm \sqrt {137}} {2}`

The roots are:

`x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}`

Answer:

`x_ {1} = \frac {-11+ \sqrt {137}} {2}\\x_ {2} = \frac {-11- \sqrt {137}} {2}`