What are the exact solutions of x² = 4 - 7x?

Solution:

The standard form of the quadratic equation ax² + bx + c = 0 and the formula used is

x = [-b ± √(b² - 4ac)]/ 2a

It is given that

x² = 4 - 7x

It can be written as

x² + 7x - 4 = 0

Here a = 1, b = 7 and c = -4

Substituting these values in the formula

x = [-7 ± √(7² - 4 × 1 × -4)]/ (2 × 1)

By further simplification

x = [-7 ± √(49 + 16)]/ 2

x = [- 7 ± √65]/ 2

Therefore, the exact solution is x = [- 7 ± √65]/ 2.

---

What are the exact solutions of x² = 4 - 7x?

Summary:

The exact solution of x² = 4 - 7x is x = [- 7 ± √65]/ 2.