Question

2x² - 4x = 1

Explanation:

Step1: Rewrite the equation

Rewrite the given equation \(2x^{2}-4x = 1\) in standard quadratic form \(ax^{2}+bx + c=0\) by subtracting 1 from both sides.
\(2x^{2}-4x - 1=0\)

Step2: Identify coefficients

For the quadratic equation \(2x^{2}-4x - 1=0\), we have \(a = 2\), \(b=- 4\), \(c=-1\)

Step3: Use quadratic formula

The quadratic formula is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\)
Substitute \(a = 2\), \(b=-4\), \(c = - 1\) into the formula:
First, calculate the discriminant \(\Delta=b^{2}-4ac=(-4)^{2}-4\times2\times(-1)=16 + 8=24\)
Then, \(x=\frac{-(-4)\pm\sqrt{24}}{2\times2}=\frac{4\pm2\sqrt{6}}{4}=\frac{2\pm\sqrt{6}}{2}=1\pm\frac{\sqrt{6}}{2}\)

Answer:

\(x = 1+\frac{\sqrt{6}}{2}\) or \(x=1 - \frac{\sqrt{6}}{2}\)