Question

x² - 2x = 3

Explanation:

Step1: Rearrange the equation

We want to set the equation to standard quadratic form \(ax^2 + bx + c = 0\). So, subtract 3 from both sides of \(x^2 - 2x = 3\) to get \(x^2 - 2x - 3 = 0\).

Step2: Factor the quadratic

We need two numbers that multiply to -3 and add to -2. The numbers are -3 and 1. So, we can factor the quadratic as \((x - 3)(x + 1)=0\).

Step3: Solve for x

Using the zero - product property, if \(ab = 0\), then either \(a = 0\) or \(b = 0\). So, we set each factor equal to zero:

• For \(x - 3=0\), we add 3 to both sides of the equation and get \(x = 3\).
• For \(x + 1=0\), we subtract 1 from both sides of the equation and get \(x=-1\).

Answer:

\(x = 3\) or \(x=-1\)