What are the roots of the equation x2 + 15x = -57 in simplest a + bi form?

Step-by-step explanation:

Rewrite x2 + 15x = -57 as x^2 + 15x + 57 = 0, in which the coefficients of this quadratic are {1, 15, 57}.

Then the discriminant is b^2 - 4ac  =  225 - 4(1)(57) = -3

Because the discriminant is negative, we know that the two roots will be complex.  They are:

      -15 ±i√3

x =

             2

9514 1404 393

  x = -7.5 ± i(√3)/2

Step-by-step explanation:

We can add (15/2)² to complete the square:

  x² +15x +(15/2)² = -57 +(15/2)²

  (x +7.5)² = -0.75

  x +7.5 = ±i(√3)/2 . . . . take the square root

The roots are ...

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step-by-step explanation: