# Solve the quadratic equation

Solving the quadratic equation is one of the most common problems that students have to solve in math. It is also one of the most difficult. The reason for this is that quadratic equations are more complex than linear equations.

## Solving the quadratic equation

There are two things you need to keep in mind when solving quadratic equations. First, remember that solutions will always involve a positive number (a solution with a negative number would be impossible). Second, remember that solutions may not be perfect. In other words, a solution may not be an exact value. This means that solutions will never be “x” exactly, but rather “x + b” or “x + b – c” where “b” and “c” are positive numbers. The formula for solving a quadratic equation is: math>left( frac{a}{x} - frac{b}{2} ight)^{2} = left( frac{a}{x} + frac{b}{2} ight)^{2}/math> where math>a/math> and math>b/math> are both positive numbers. To solve a quadratic equation step by step, you follow these three steps: Step 1 – Identify if your quadratic equation

Solve the quadratic equation by creating a table of values. The first step is to write the equation in standard form, with both terms on the left-hand side. The second step is to place the left-hand side of the equation in parentheses and solve for "c". In most cases, this will require dividing both sides of the equation by "b". Thus, solving for "c" involves finding a value for "b" that satisfies the two inequalities: Once you have found a value for "b", then you can use it to find a solution for "c". In some cases you may be able to find all three solutions at once. If there are multiple solutions, choose the one that gives you the smallest value for "c". In other words, choose the solution that minimizes the squared distance between your points and your line. This will usually be either (1/2) or 0.5, depending on whether your line is horizontal or vertical. When you've found all three solutions, then use them to construct a table of values. Remember to include both x and y coordinates so that you can see how far each solution has moved (in terms of x and y). You can also include the original value for c if you want to see how much your points have moved relative to each other. Once you've constructed your table,

The quadratic equation is an example of a non-linear equation. Quadratics have two solutions: both of which are non-linear. The solutions to the quadratic equation are called roots of the quadratic. The general solution for the quadratic is proportional to where and are the roots of the quadratic equation. If either or , then one root is real and the other root is imaginary (a complex number). The general solution is also a linear combination of the real roots, . On the left side of this equation, you can see that only if both are equal to zero. If one is zero and one is not, then there must be a third root, which has an imaginary part and a real part. This is an imaginary root because if it had been real, it would have squared to something when multiplied by itself. The real and imaginary parts of a complex number represent its magnitude and its phase (i.e., its direction relative to some reference point), respectively. In this case, since both are real, they contribute to the magnitude of ; however, since they are in opposite phase (the imaginary part lags behind by 90° relative to the real part), they cancel each other out in phase space and have no effect on . Thus, we can say that . This representation can be written in polar form