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Solving Quadratic Equations by Factoring

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Solving Quadratic Equations by Factoring

Quadratic equations are equations that have a term with the variable squared. They can be written in the standard form ax2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0. Solving a quadratic equation means finding the values of x that make the equation true.

One way to solve a quadratic equation is by factoring. Factoring involves finding two expressions that multiply together to give the original quadratic expression. Once you have factored the quadratic, you can set each factor equal to zero and solve for x.

Steps for Solving Quadratic Equations by Factoring

  1. Write the quadratic equation in standard form. This means that the equation should be in the form ax2 + bx + c = 0.
  2. Factor the quadratic expression. This means finding two expressions that multiply together to give the original quadratic expression.
  3. Set each factor equal to zero.
  4. Solve for x.

Example

Let's solve the quadratic equation x2 - 9 = 0 by factoring.

  1. The equation is already in standard form.
  2. We can factor the quadratic expression as (x + 3)(x - 3).
  3. Setting each factor equal to zero, we get x + 3 = 0 and x - 3 = 0.
  4. Solving for x, we get x = -3 and x = 3.

Therefore, the solutions to the quadratic equation x2 - 9 = 0 are x = -3 and x = 3.

Additional Resources

If you're looking for more information on solving quadratic equations, check out these resources:

Conclusion

Solving quadratic equations by factoring is a useful technique that can be used to find the solutions to many different quadratic equations. By following the steps outlined above, you can successfully factor and solve quadratic equations.

quadratic equations