# What are the exact solutions of x^{2} = 4 - 7x?

**Solution:**

The standard form of the quadratic equation ax^{2} + bx + c = 0 and the formula used is

x = [-b ± √(b^{2} - 4ac)]/ 2a

It is given that

x^{2} = 4 - 7x

It can be written as

x^{2} + 7x - 4 = 0

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

Substituting these values in the formula

x = [-7 ± √(7^{2} - 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 x^{2} = 4 - 7x?

**Summary:**

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

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