Question

Solve for x in the equation x² + 14x + 17 = - 96

Answer 1

Solutions of x are;

x = -7 + 8i and x = -7 -8i

Explanation:

Given the equation:
`x^2+14x+17 = -96`

Add 96 both sides we get;

`x^2+14x+17+96 = 0`

`x^2+14x+113= 0`

Using quadratic formula
`ax^2+bx+c = 0` then the solution is given by:

`x = (-b\pm√(b^2-4ac))/(2a)`

On comparing we have;

a= 1, b =14 and c =113

`x = (-14\pm√((14)^2-4(1)(113)))/(2(1))`

`x = (-14\pm√(196-452))/(2)`

or

`x = (-14\pm√(-256))/(2)`

Simplify:

`x = (-14\pm 16i)/(2)` ; where i is the imaginary,
`i^2= -1`

or

`x = -7 \pm 8i`

Therefore, the solution of x are; x = -7 + 8i and x = -7 -8i