Question

solve for x. separate multiple answers with a comma. x² - 9x + 20 = 0

Explanation:

Step1: Factor the quadratic equation

We need to find two numbers that multiply to \(20\) and add up to \(-9\). The numbers are \(-4\) and \(-5\) because \((-4)\times(-5) = 20\) and \((-4)+(-5)=-9\). So we can factor the quadratic as:
\(x^{2}-9x + 20=(x - 4)(x - 5)=0\)

Step2: Solve for \(x\) using zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\).
For \((x - 4)(x - 5)=0\), we set each factor equal to zero:

• If \(x - 4=0\), then \(x=4\).
• If \(x - 5=0\), then \(x = 5\).

Answer:

\(4,5\)