# What are the Exact Solutions of x^{2} = 4 − 7x?

We will be using the formula of roots of a quadratic equation to answer this.

## Answer: The exact solutions of x^{2} = 4 − 7x are x = (-7 ±√65)/2

Let's solve this step by step.

**Explanation:**

The roots of a quadratic equation ax^{2} + bx + c = 0 are given by:

x = \(\begin{align} \frac{-b \pm \sqrt{b^2-4ac}}{2a}\end{align}\)

x^{2} = 4 − 7x

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

Therefore, a =1, b = 7, c = -4.

d^{2} = b^{2} - 4ac = 7^{2} - 4 × 1 × (-4)

d^{2} = 49 + 16

d^{2} = 65

d = ±√65 .

There are 2 real roots:

x = (-b ± d)/2a

x = (-7 ±√65)/2