Question

solve for all values of x by factoring.

x² - 81 = 0

answer attempt 1 out of 2

Explanation:

Step1: Recognize difference of squares

The equation \(x^2 - 81 = 0\) is a difference of squares, since \(x^2\) is a square and \(81 = 9^2\). The formula for factoring a difference of squares is \(a^2 - b^2=(a - b)(a + b)\). Here, \(a = x\) and \(b = 9\), so we factor the left - hand side as \((x - 9)(x + 9)=0\).

Step2: Apply zero - product property

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

• For \(x - 9=0\), we solve for \(x\) by adding 9 to both sides of the equation. We get \(x=9\).
• For \(x + 9=0\), we solve for \(x\) by subtracting 9 from both sides of the equation. We get \(x=- 9\).

Answer:

\(x = 9\) or \(x=-9\)