# Problem Solving Using Quadratic Equations

To use the Quadratic Formula, we substitute the values of into the expression on the right side of the formula.Then, we do all the math to simplify the expression.

So factoring out −2 will result in the common factor of (r – 3).

If we had gotten (−r 3) as a factor, then when setting that factor equal to zero and solving for r we would have gotten: There are many applications for quadratic equations.

We will see in the next example how using the Quadratic Formula to solve an equation with a perfect square also gives just one solution.

When we solved the quadratic equations in the previous examples, sometimes we got two solutions, sometimes one solution, sometimes no real solutions.

Is there a way to predict the number of solutions to a quadratic equation without actually solving the equation?

Yes, the quantity inside the radical of the Quadratic Formula makes it easy for us to determine the number of solutions.

Now, we will go through the steps of completing the square in general to solve a quadratic equation for .

It may be helpful to look at one of the examples at the end of the last section where we solved an equation of the form as you read through the algebraic steps below, so you see them with numbers as well as ‘in general.’ This last equation is the Quadratic Formula.

We cannot take the square root of a negative number.

So, when we substitute , , and into the Quadratic Formula, if the quantity inside the radical is negative, the quadratic equation has no real solution. The quadratic equations we have solved so far in this section were all written in standard form, .

• ###### Solving Problems using the Quadratic Formula -

Test your knowledge of solving problems using the quadratic formula by using this interactive quiz. Utilize the worksheet to identify the more.…

• ###### How to Solve Word Problems Using Quadratic Equations

How to Solve Word Problems Using Quadratic Equations, Ch. 5.2, Algebra 2 Advanced.…

Solve quadratic equations using the quadratic formula. For example, solve -9x+10x²+8=14. If you're seeing this message, it means we're having trouble loading external resources on our website.…

• ###### Solve a Quadratic Equation Using the Quadratic Formula - WebMath

Solve a Quadratic Equation Using the Quadratic Formula This page will show you how to use the quadratic formula to get the two roots of a quadratic equation. Fill in the boxes to the right, then click the button to see how it’s done.…

Quadratic Equation Word Problems Worksheet with Answers Worksheet given in this section is much useful to the students who would like to practice solving word problems on quadratic equation. Quadratic Equation Word Problems Worksheet with Answers - Problems. Problem 1 Difference between a number and its positive square root is 12. Find the.…

• ###### Word Problems Involving Quadratics - sites.millersville.edu

Word Problems Involving Quadratics. These word problems involve situations I've discussed in other word problems The area of a rectangle, motion time, speed, and distance, and work. However, these problems lead to quadratic equations. You can solve them by factoring or by using the Quadratic Formula.…

• ###### Solve quadratic equation with Step-by-Step Math Problem Solver

Solve word problems involving quadratic equations. Certain types of word problems can be solved by quadratic equations. The process of outlining and setting up the problem is the same as taught in chapter 5, but with problems solved by quadratics you must be very careful to check the solutions in the problem itself.…