Chapter 4, Problem 22AR

To determine

To solve the given equation, $x^2+2x-1=0$ by factoring or quadratic formula.

Answer to Problem 22AR

  $x=-1+\sqrt{2},-1-\sqrt{2}$

Explanation of Solution

Given:

The equation is, $x^2+2x-1=0$

Calculation:

We can solve the given equation by using quadratic formula.

That is,

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

The given equation $x^2+2x-1=0$ , which is in the form of $a{x}^2+bx+c=0$ . Where, $a=1,b=2\text{ and c =-1}$

Now, Substitute the values in the formula then we get that,

  $\begin{array}{l}x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}\\ x=\frac{-\left(2\right)\pm \sqrt{{\left(2\right)}^2-4\left(1\right)\left(-1\right)}}{2\left(1\right)}\\ x=\frac{-\left(2\right)\pm \sqrt{4+4}}{2}\\ x=\frac{-\left(2\right)\pm \sqrt{8}}{2}\\ x=\frac{-2\pm 2\sqrt{2}}{2}\\ x=-1\pm \sqrt{2}\\ x=-1+\sqrt{2},-1-\sqrt{2}\end{array}$

Therefore, the roots for the given equation, $x^2+2x-1=0$ are $x=-1+\sqrt{2},-1-\sqrt{2}$ .