Question

A quadratic equation is shown: x2 + 18x + 76 = 0 Which of the following is the first correct step to write the above equation in the form (x − p)2 = q, where p and q are integers? x2 + 18x + 76 + 9 = 0 + 9 x2 + 18x + 76 + 5 = 0 + 5 x2 + 18x + 76 − 5 = 0 − 5 x2 + 18x + 76 − 9 = 0 − 9

Answer 1

Answer:

  x^2 + 18x + 76 + 5 = 0 + 5

Step-by-step explanation:

The first step is to determine the constant that is needed to be able to write the expression in the desired form. That constant is the square of half the x-term coefficient: (18/2)^2 = 9^2 = 81.

The constant that is present is 76, which is 5 fewer than the needed constant, so the "first step" is to add 5 to both sides of the equation:

  x^2 + 18x + 76 + 5 = 0 + 5

Then the next step would be to write the left side as a square:

  (x +9)^2 = 5 . . . . . . . p = -9; q= 5