Solve the Equation: Finding x in x² + x = 0

Quadratic Equations with Factoring Method

Find the value of the parameter x.

x2+x=0 x^2+x=0

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's solve this math problem together.
00:08 First, we break it down into smaller factors.
00:16 Now, look for any common factor we can take out.
00:27 Then, find out what makes each factor equal to zero.
00:31 Isolate the unknown variable. This gives us one solution. Let's find the second one.
00:39 And that's how we find the solution to the question. Nice work!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Find the value of the parameter x.

x2+x=0 x^2+x=0

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Factor the equation x2+x=0 x^2 + x = 0 .
  • Step 2: Use the Zero-Product Property to solve for x x .

Now, let's work through each step:

Step 1: Start by factoring the left-hand side of the equation:
x2+x=x(x+1) x^2 + x = x(x + 1)

Step 2: Apply the Zero-Product Property:
Since x(x+1)=0 x(x + 1) = 0 , we have two possible equations:
1) x=0 x = 0
2) x+1=0 x + 1 = 0

For the second equation, solve for x x :
x+1=0 x + 1 = 0 implies x=−1 x = -1

Therefore, the solutions to the equation are x=0 x = 0 and x=−1 x = -1 .

Hence, the value of the parameter x x is x=0,x=−1 x = 0, x = -1 .

3

Final Answer

x=0,x=−1 x=0,x=-1

Key Points to Remember

Essential concepts to master this topic
  • Factoring Rule: Extract common factors from all terms first
  • Zero-Product Property: If x(x+1)=0 x(x + 1) = 0 , then x = 0 or x + 1 = 0
  • Verification: Check both solutions: 02+0=0 0^2 + 0 = 0 and (−1)2+(−1)=0 (-1)^2 + (-1) = 0 ✓

Common Mistakes

Avoid these frequent errors
  • Dividing both sides by x without considering x = 0
    Don't divide x2+x=0 x^2 + x = 0 by x to get x + 1 = 0! This eliminates the solution x = 0 and gives only x = -1. Always factor out x first, then use the Zero-Product Property to find all solutions.

Practice Quiz

Test your knowledge with interactive questions

Find the value of the parameter x.

\( x^2+x=0 \)

FAQ

Everything you need to know about this question

Why can't I just divide both sides by x?

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Dividing by x is dangerous because x could equal zero! When you divide by a variable, you might lose valid solutions. Always factor first to see all possibilities.

How do I know when to use the Zero-Product Property?

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Use it whenever you have a product equal to zero. If A×B=0 A \times B = 0 , then either A = 0 or B = 0 (or both).

What if I can't factor the expression easily?

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For x2+x=0 x^2 + x = 0 , always look for the greatest common factor first. Here, both terms have x as a factor, so factor out x!

Do quadratic equations always have two solutions?

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Not always! Some have two different solutions (like this one), some have one repeated solution, and some have no real solutions at all.

How can I check if my solutions are correct?

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Substitute each solution back into the original equation. For x = 0: 02+0=0 0^2 + 0 = 0 ✓. For x = -1: (−1)2+(−1)=1−1=0 (-1)^2 + (-1) = 1 - 1 = 0 ✓

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