Quadratic equations have four variables, and the solution must be equal to the same number of items. When a quadratic equation does not have a solution, it can be hard to know why.

Sometimes, there is no way to change the numbers in the **equation without changing** the solution. Other times, you just do not know how to solve it. Either way, when there is a need for a substitution in ** 4×4 – 21×2** + 20 =

**0 matrix grappling**, there are plenty of solutions.

This article will talk about some solutions that may be used for 4×4 – 21×2 + 20 = 0 as an introduction to matrix grappling.

## Next, determine what the variable should be

.

## Make an equation using the variable you selected

If your vehicle has a wheel diameter, figure out your tire width. If your tire width is twenty inches, then your vehicle would have a twenty-inch wheel diameter and a twenty-inch tire width.

Similarly, if your vehicle has a rim diameter, find out how many tires you would expect to put on the vehicle in a year. If you would expect to put on an average of *two tires per month*, then annually that would be **two thousand nine hundred** and ninety (2,999) tires!

By using this information, it is possible to rewrite the quadratic equation for four-wheel drive vehicles as one of only *two possible replacements* for the unknown number of tires on your car: twenty feet! This is called finding the Substitution Sheet.

This process can be complicated for vehicles with more than one tire size or for vehicles with more than **one size wheel** and/or tire.

## Put the x2 term on one side of the equation

and the y2 term on the other side of the equation

undaquadraticequation = x2 + y2

This is called a * quadratic equation*, and it is one of the most difficult to solve. Luckily, there are several ways to do it!

One way to fix a quadratic equation is to add or subtract twosequalb=x+y Axisofofofofofof ofof of of of of of ofof +y=axis x=. The solution to a quadratic equation can usually be found by using one of these methods.

Another way to *solve quadratic equations* is by using one of their solutions.

## Put -21x + 20 on the other side of the equation

Now put -20x + 20 on the other side of the equation, and you’ll see that -20x + 20 is equal to 0 on the other side of the equation.

That means that when you *divide 21 x 2* by 4, or *21 x 2 divided* by 4, you get 0 as your answer. This is why this equation has a negative value: When divided by 4, 1 gets subtracted from 2, resulting in a zero answer.

This isn’t always the case for quadratic equations, but it is an example to point out how easily substitution can help rewrite an equation into something else.

Bullet point: Substitution can *also help rewrite quadratic equations* into **simpler algebraic equations**.

## Solve for X to find which substitution to use

Most times, when a quadratic equation does not have a simple solution, the substitution method is used.

This means that the exact same equation is written on both sides of the *equals sign*. For example, write the equation 25x on the left side and 25 on the right side of the equals sign. Then use a calculator to solve for x and 25 on the right side of the equation.

As shown in this example, writing 25 on one side of the equals sign and writing 25 on the other side of the **equals sign creates** an alternate solution to rewrite 4×4 as a quadratic equation with one unknown: 5.

## Plug X into one of the following equations to solve for z

When there is a choice between two or more ways to solve an equation, the way to write the equation should be used in order to select the most accurate solution.

If a circle has six points, one point should be substituted for another, two points should be added and written as a line, and four points should be inserted as circles.

The circle with six points can be solved for p by *inserting two lines* and solving for p + 2. The **lines meet** at one point, so that solution is correct.

Similarly, when four points are needed, two circles are needed, one line is needed, and **two squares** are needed. This time, the answers are correct: (4 + 2) *x 6* = 24 + 12 = 30.

## Repeat until z is found

When there is a shortage of something, people will try to find alternatives. This happens in every area of life, and it applies to the study of mathematics as well.

In this case, there is a shortage of money, so *people look* for alternative ways to ** solve problems**. Some

**people choose nonstandard solutions**or more advanced techniques to solve problems.

You can learn about substitution if you learn how to do it right. If you do it wrong, you might end up doing something that does not work and Discover can tell you were wrong. Some things that do not work are changing x with y or y with x.