Quadratic Equation Basics: Solving x² + x = 0

Solve the following equation:

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
00:00 Find X
00:03 Factor X squared into factors X and X
00:09 Find the common factor
00:21 Take out the common factor from the parentheses
00:25 Find what makes each factor in the product equal to 0
00:31 This is one solution
00:36 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Solve the following equation:

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

2

Step-by-step solution

To solve the equation x2+x=0 x^2 + x = 0 , we will use a step-by-step method:

  • Step 1: Identify the equation form.
    The equation given is x2+x=0 x^2 + x = 0 . This is a quadratic equation in a simpler form since it can be factored easily.
  • Step 2: Factor the equation.
    We notice that both terms of the equation have a common factor, which is x x . Therefore, we can factor out x x as follows:

x(x+1)=0 x(x + 1) = 0

  • Step 3: Apply the zero product property.
    The zero product property tells us that if the product of two factors is zero, then at least one of the factors must be zero. Thus, set each factor equal to zero:

x=0 x = 0
x+1=0 x + 1 = 0

  • Step 4: Solve each equation.
    The first equation gives x=0 x = 0 directly. The second equation can be solved by subtracting 1 from both sides to find:

x=1 x = -1

Therefore, the solutions to the equation x2+x=0 x^2 + x = 0 are x1=0 x_1 = 0 and x2=1 x_2 = -1 .

Therefore, the correct answer is:

x1=0,x2=1 x_1 = 0, x_2 = -1

3

Final Answer

x1=0,x2=1 x_1=0,x_2=-1

Practice Quiz

Test your knowledge with interactive questions

a = Coefficient of x²

b = Coefficient of x

c = Coefficient of the independent number


what is the value of \( a \) in the equation

\( y=3x-10+5x^2 \)

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