Solve the Quadratic Equation by Factoring: 3x^2 - 9x = 0

Video Solution

Solution Steps

00:00 Find X

00:03 Factor X squared into factors X and X

00:11 Factor 9 into factors 3 and 3

00:18 Find the common factor

00:34 Take out the common factor from the parentheses

00:40 Find what makes each factor in the product zero, so it equals 0

00:46 Isolate X, this is one solution

00:51 Now we'll use the same method and find the second solution

01:05 And this is the solution to the question

Step-by-Step Solution

To solve the equation $3x^2 - 9x = 0$ , we will factor the quadratic expression:

Step 1: Factor the quadratic.
Observe that both terms in $3x^2 - 9x$ have a common factor of $3x$ . Thus, we factor by pulling out $3x$ :
$3x(x - 3) = 0$
Step 2: Apply the zero product property.
According to the zero product property, if $3x(x - 3) = 0$ , then either $3x = 0$ or $x - 3 = 0$ must hold true.
Step 3: Solve each factor for $x$ .
- For $3x = 0$ :
Divide both sides by 3:
$x = 0$
- For $x - 3 = 0$ :
Add 3 to both sides:
$x = 3$

Therefore, the solutions to the equation are $x_1 = 3$ and $x_2 = 0$ .

These solutions correspond to the choice: $x_1=3,x_2=0$ .