Question

Write the equation so that

a = 1: x2 +
-6
x
=
-13

Complete the square:

x2 – 6x +
=
–13 +

Answer 1

x = 2i + 3 or -2i + 3

Explanation:

Solving equation by completing the square:

x² - 6x = -13

1.Divide the coefficient of x by 2.

6 ÷ 2 = 3

2. Find the square of the result of step 1 and add it to both sides.

1. (3)² = 9

1. x² - 6x + 9 = -13 + 9
2. x² - 2*x * 3 + 3² = -4
3. (x - 3)² = (2i)² {i² = -1}
4. Take square root,
5. x - 3 = ±2i
6. x -3 = 2i or x - 3 = -2i
7. x = 2i+3 ; x = -2i + 3