Question

use the quadratic formula to solve.
0.5x² - 1x - 0.5 = 0

Explanation:

Step1: Recall quadratic formula

The quadratic formula for a quadratic equation \(ax^2 + bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For the equation \(0.5x^{2}-1x - 0.5=0\), we identify \(a = 0.5\), \(b=- 1\), and \(c=-0.5\).

Step2: Calculate discriminant (\(D=b^{2}-4ac\))

Substitute \(a = 0.5\), \(b = - 1\), \(c=-0.5\) into the discriminant formula:
\(D=(-1)^{2}-4\times0.5\times(-0.5)\)
\(=1 + 1\)
\(=2\)

Step3: Substitute into quadratic formula

Now substitute \(a = 0.5\), \(b=-1\), and \(D = 2\) into the quadratic formula:
\(x=\frac{-(-1)\pm\sqrt{2}}{2\times0.5}=\frac{1\pm\sqrt{2}}{1}=1\pm\sqrt{2}\)

Answer:

\(x = 1+\sqrt{2}\) or \(x=1 - \sqrt{2}\)