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

x = 8i - 7    or  x= -8i - 7

Step-by-step explanation:

To solve;

x²  +   14x + 17 = -96

We can rearrange this;

Subtract 17 from both-side of the equation

x²  +   14x + 17-17 = -96-17

x²  +   14x  = -113

We can not use factorization method to so this quadratic equation but we can use completing the square method or formula method to solve.

In this case we are going to be using completing the square method to solve;

x²  +   14x  = -113

Add the square of half of the coefficient of x to both-side of the equation

(That is; the coefficient of x is 14, half of 14 is 7, so we will add 7² to both-side of the equation)

x²  +   14x  + (7)² = -113 + 7²

We will factor  the left hand-side of the equation and the si mplify the right-hand side of the equation.

(x + 7)²  =  -113 + 49

(x + 7)²  = -64

Take the square root of both-side of the equation

   = ±

x + 7 = ±

We cant take the square root of negative number, so we will separate the negative integer from the positive integer.

x + 7 =    ×    

x + 7 =  ×  ±8

Note i

x + 7 = i ×  ±8

x + 7 = ±8i

Subtract 7 from both-side of the equation

x + 7 -7 = ±8i - 7

x =  ±8i - 7

Either x = 8i - 7          OR     x = -8i - 7