Equations which equal 0

All we need to do is isolate x as we would when trying to solve for x in any equation, then take the square root of a constant. Solving equations using factoring relies on using one of the properties of 0. If the product of two numbers, or expressions, is 0, then at least one of the expressions must equal 0.

This allows us to separate the factors and set them equal to 0 individually to find the solution s to the equation. In this case, even though we are taking a square root, 0 is neither positive nor negative, so there is only one solution. The terms "quadratic formula" and "quadratic equation" are sometimes used interchangeably, but the two should not be confused. The quadratic formula refers specifically to a formula used to solve quadratic equations:.

The quadratic formula can be thought of as a "brute force" method for solving quadratic equations since it can be used to solve any quadratic equation in standard form, like all of the examples above.

Dividing through by the factor x makes the implicit assumption that x was not equal to zero. There is absolutely no justification for making that assumption!

And making that assumption would cause us to lose half of our solution to this equation. I need to remember that it's okay for a factor to contain only a variable, without being added to other terms; in particular, " x " is a perfectly valid factor. I need to set both of the factors equal to zero, and then solve the two resulting linear equations:. The previous example had two terms and was easy to factor. There is one other case of two-term quadratics that we can factor to solve.

It's only a bit more complicated:. This equation is in " quadratic equals zero " form, so it's ready for me to solve by factoring. But how do I factor this?

By noticing that this is a difference of squares. I'll apply the difference-of-squares formula that I've memorized:. This is pronounced as " x is equal to plus or minus 2 ".

The last example above leads us into how to solve by taking square roots, on the next page. You can use the Mathway widget below to practice solving quadratic equations by factoring.

Try the entered exercise, or type in your own exercise. Then click the button and select "Solve by factoring" to compare your answer to Mathway's. Or skip ahead to the next page. Please accept "preferences" cookies in order to enable this widget.

Click "Tap to view steps" to be taken directly to the Mathway site for a paid upgrade. All right reserved. Web Design by. Skip to main content. Purplemath This lesson covers many ways to solve quadratics, such as taking square roots, completing the square, and using the Quadratic Formula.

Here's how it works: Content Continues Below. Content Continues Below. DaleSwanson DaleSwanson 1 1 silver badge 6 6 bronze badges. I didn't get it, when will we need to multiply by 0? Add a comment. But think about what you end up with. Fly by Night Fly by Night David Farmilant 75 10 10 bronze badges. James S. Cook James S. Cook Argon Argon Finding the solutions means finding the x,0 point value s Hope this conceptual understanding helps you as much as it did me!

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