Question

values of x by factoring.

\tx² - 6x - 105 = -6x - 5

attempt 1 out of 2

Explanation:

Step1: Simplify the equation

First, we want to get all terms on one side of the equation. Add \(6x\) and \(5\) to both sides of the equation \(x^{2}-6x - 105=-6x - 5\).
\(x^{2}-6x+6x - 105 + 5=-6x+6x - 5 + 5\)
Simplifying the left - hand side and the right - hand side, we have \(x^{2}-100 = 0\) (because \(-6x + 6x=0\) and \(-105 + 5=-100\)).

Step2: Factor the quadratic

We recognize that \(x^{2}-100\) is a difference of squares. The formula for the difference of squares is \(a^{2}-b^{2}=(a + b)(a - b)\). In this case, \(a = x\) and \(b = 10\) (since \(100=10^{2}\)), so \(x^{2}-100=(x + 10)(x - 10)\). Our equation becomes \((x + 10)(x - 10)=0\).

Step3: Solve for x

Using the zero - product property, which states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\).

• If \(x+10 = 0\), then \(x=-10\).
• If \(x - 10=0\), then \(x = 10\).

Answer:

The values of \(x\) are \(x=-10\) and \(x = 10\)