# Which of the following is a solution of x^{2 }- 10x = -36?

10 + 2i√11, 5 + i√11, 5 - i√11, 10 - 2i√11

**Solution:**

The given __equation__ is

x^{2 }- 10x + 36 = 0

The above equation is a __quadratic equation__ of the form ax^{2} + bx + c

The __roots__ of the equation a^{2} + bx + c are:

(-b ± √b^{2} - 4ac)/2a

Here a = 1, b = -10, c = 36

b^{2} - 4ac = 10^{2} - 4(1)(36) = 100 - 144 = -44

Therefore

√b^{2} - 4ac = √-44 = √-4 × 11 = 2√11 × -1 = 2√11 × √-1 = 2i√11 (√-1 = i)

The roots of the given equation are 5 + i√11 and 5 - i√11 which are complex conjugates.

## Which of the following is a solution of x^{2 }- 10x = -36?

**Summary:**

The roots of the given equation are 5 + i√11 and 5 - i√11 which are complex conjugates.

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