Question

Type the correct answer in each box. Use numerals instead of words. Consider the quadratic equation x2 + 10x + 27 = 0. Completing the square leads to the equivalent equation (x + )2 = .

Answer 1

Answer:

Step-by-step explanation:

ax² + bx + c = y

x² + 10x + 27 = 0

to complete the square, we want the "c" term to be equal to the square of half of the "b" term.

In this case b = 10, half of that is 5. the square of 5 is 25.

We already have c = 27, so to get 25 there we just subtract 2 from each side of the equation.

x² + 10x + 27 - 2 = 0 - 2

x² + 10x + 25 = - 2

         (x + 5)² = - 2

taking the square root of each side

            x + 5 = ±√- 2

the square root of a negative number is an imaginary number

            x + 5 = ±√-1√2

            x + 5 = ± i√2

                  x = - 5 ± i√2