# What is the positive solution to the equation 0 = –x^{2} + 2x + 1? Use the quadratic formula.

A quadratic equation is an equation that is in the form of ax^{2 }+ bx + c = 0 where a ≠ 0. They have many applications in various fields of engineering and science, and are used to fin values of various quantities and parameters

## Answer: The positive solution to the equation –x^{2} + 2x + 1 = 0 is x = 1 + √2.

Let's solve step by step to find the solutions of this quadratic equation.

**Explanation:**

Given that –x^{2} + 2x + 1 = 0

⇒ Multiplying by -1 on both sides, we get x^{2} - 2x - 1 = 0

The quadratic formula is given by x = (-b ± √ (b^{2} - 4ac)) / 2

As we know that coefficient of x^{2 } is a, coefficient of x is b and the constant term is c.

So, a = 1, b = - 2 and c = - 1

Using the quadratic formula, we get,

⇒ x = - (-2) ± √ ((- 2)^{2 }- 4 (1) (-1)) / 2 (1)

⇒ x = - (-2) ± √ (4^{ }+ 4) / 2

⇒ x = - (-2) ± √ (8) / 2

On finding the square root, we will have two values of 'x'.

⇒ x = (2 + 2√2) / 2 or x = (2 - 2√2) / 2

⇒ x = 1 + √2 or x = 1 - √2

Hence, we see that 1 + √2 = 1 + 1.414 = 2.414, which is positive; and 1 - √2 = 1 - 1.414 = -0.414, which is negative.