* The length is 3 more than twice the width, so The area is 560, so Plug in and solve for W: Use the Quadratic Formula: Since the width can't be negative, I get . Calvin and Bonzo can eat 1260 hamburgers in 12 hours. If Calvin and Bonzo eat together, they can eat 480 hot dogs in 6 hours. Plug these into the first equation and solve for t: The solutions are and . Calvin rides his power boat up and down a drainage ditch.*We're going to learn the steps to solving a quadratic equation by factoring, completing the square, and using the quadratic formula.The discriminant is the value under the radical sign, b – 4 ac is 0, the equation has one root.

* The length is 3 more than twice the width, so The area is 560, so Plug in and solve for W: Use the Quadratic Formula: Since the width can't be negative, I get . Calvin and Bonzo can eat 1260 hamburgers in 12 hours. If Calvin and Bonzo eat together, they can eat 480 hot dogs in 6 hours. Plug these into the first equation and solve for t: The solutions are and . Calvin rides his power boat up and down a drainage ditch.We're going to learn the steps to solving a quadratic equation by factoring, completing the square, and using the quadratic formula.The discriminant is the value under the radical sign, b – 4 ac is 0, the equation has one root.*

There are many ways to solve quadratic equations, such as through factoring, completing the square, or using the quadratic formula.

In the following section, we will demonstrate using the quadratic formula.

However, these problems lead to quadratic equations.

You can solve them by factoring or by using the Quadratic Formula.

The two values that we found via factoring, x = −4 and x = 3, lead to true statements: 0 = 0. But x = 5, the value not found by factoring, creates an untrue statement—27 does not equal 0!

Note in the example above, if the common factor of 2 had been factored out, the resulting factor would be (−r 3), which is the negative of (r – 3).

When using the quadratic formula, you should be aware of three possibilities.

These three possibilities are distinguished by a part of the formula called the discriminant.

This is generally true when the roots, or answers, are not rational numbers.

A second method of solving quadratic equations involves the use of the following formula: , b is the numeral that goes in front of x, and c is the numeral with no variable next to it (a.k.a., “the constant”).

## Comments Solving Quadratic Equations Problems

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