What number needs to be added to both sides of the equation in order to complete the square? x2+14x=−32

      49 is the number to be added to both the sides of the equation to complete the square.

   The equation given in the question is

Which can be written as  

We have to convert it into square form.

  Since the standard form of the equation in square form is

(a + b)² = a² + 2ab + b²

By comparing this standard equation with the given equation,

a = x

&

b = 7

By substituting the values of 'a' and 'x' in the standard square form,

x² + 14x + 7² = -(32) + 7²

x² + 14x + 49 = -32 + 49

(x + 7)² = 17

     Therefore, 49 should be added in both the sides of the equation in order to complete the square.

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