#WAYS TO SOLVE QUADRATIC EQUATIONS HOW TO#

#WAYS TO SOLVE QUADRATIC EQUATIONS HOW TO#

If there is a limited amount of space and we desire the largest monitor possible, how do we decide which one to choose? In this section, we will learn how to solve problems such as this using four different methods.Īn equation containing a second-degree polynomial is called a quadratic equation. Proportionally, the monitors appear very similar. The left computer monitor in the image below is a 23.6-inch model and the one on the right is a 27-inch model. Use the discriminant to determine the number and type of solutions to a quadratic equation.Use the quadratic formula to solve a quadratic equation.Complete the square to solve a quadratic equation.Use the Pythagorean Theorem and the square root property to find the unknown length of the side of a right triangle.Use the square root property to solve a quadratic equation.Factor a quadratic equation to solve it.With practice, solving quadratic equations can become second nature.By the end of this section, you will be able to: No matter which method you choose to solve quadratic equations, understanding and practicing each technique will build a strong foundation for tackling more complex mathematical problems. Step 4: Read off or approximate these intersection points (x-values) as your solutions. Step 3: Determine where the curve intersects with the x-axis. Step 2: Plot the parabola to form a curve on a graph. Step 1: Convert the given equation into slope-intercept form (y = ax² + bx + c). Here’s how to find solutions using graphing: By sketching the parabolic function representing the equation on a graph, you can identify where it crosses the x-axis, indicating its solutions. Using graphs is a visual method to solve quadratic equations. Step 4: Calculate both possible values for x by choosing either ‘+’ or ‘-‘ in the formula. Step 3: Simplify the expression under the square root (b²-4ac). Step 2: Plug these values into the quadratic formula. By simply plugging the coefficients into this formula, you can solve for x. This well-known formula is defined as x = (-b ± √(b²-4ac)) / 2a. The quadratic formula is a universally applicable method for solving quadratic equations.

Step 5: Take the square root of both sides and rearrange for x. Step 4: Factor the resulting perfect square trinomial on one side of the equation Step 3: Add the square of half of ‘b’ to both sides, creating a perfect square trinomial. Step 2: Move ‘c’ to the other side of the equation. This is an interesting way to solve quadratic equations. Thus B/2 &pm z will be the two roots to the original equation. Once you have z, you can add B/2 and that gives two values with the desired sum B and product C. Step 1: Divide the quadratic equation by ‘a’ to ensure a leading coefficient of one. Then you can solve for z by setting the product, which will be a difference of squares, equal to C. This process converts the quadratic equation into a perfect square trinomial which allows for easier solving. Step 5: Set each factor equal to zero and solve for x.Ĭompleting the square is another method that works for any type of quadratic equation. Step 3: Write out the factors by replacing b with the two numbers discovered in step 2. Step 2: Determine two numbers whose product is equal to ac and whose sum is equal to b. Step 1: Identify the coefficients (a, b, and c) in the equation.

Here’s a step-by-step guide on how to factor a quadratic equation: Factoring is most useful when the quadratic equation can be easily decomposed into whole numbers. When multiplied together, these factors produce the original equation.

Here are four ways to solve quadratic equations:įactoring is a technique that involves breaking down a quadratic equation into two simpler expressions, known as factors. These equations, represented by ax² + bx + c = 0, may seem daunting at first, but with the right tools, they can be easily tackled. Quadratic equations are essential in the world of mathematics and can often form barriers for students in their mathematical journeys.

Ways to solve quadratic equations