Solve the Cubic Equation: x³ + x² - 12x = 0

Question

$x^3+x^2-12x=0$

00:05 Let's find X.

00:08 First, factor out using X.

00:19 Take out the common factor from the parentheses.

00:36 This gives us one solution that makes the equation zero.

00:42 Now let's solve the second factor.

00:49 Factor the trinomial by identifying the coefficients.

00:54 Find two numbers whose sum is B, which is 1.

00:59 And whose product is C, which is negative twelve.

01:05 These are the numbers we need. Substitute them into the parentheses.

01:10 Find what makes each factor zero.

01:15 And that's how we solve this problem!

To solve the equation $x^3 + x^2 - 12x = 0$ , follow these steps:

Step 1: Factor out the greatest common factor. The common factor here is $x$ .
Step 2: The equation becomes $x(x^2 + x - 12) = 0$ .
Step 3: Apply the zero-product property. This gives us two equations to solve: $x = 0$ and $x^2 + x - 12 = 0$ .
Step 4: Solve $x = 0$ . This is a straightforward solution: $x = 0$ .
Step 5: Solve the quadratic equation $x^2 + x - 12 = 0$ . We will factor it:

Therefore, the solutions to the equation are $x = 0$ , $x = 3$ , and $x = -4$ .

Thus, the complete solution set for $x$ is $x = 0, 3, -4$ .

$x=0,3,-4$