Solution of Equation

Equations which involve unknowns raised to a power of one are known as first degree equations. Second degree equations also exist which involve at least one variable that is squared, or raised to a power of two. Equations can also be third degree, fourth degree, and so on. The most famous second degree equation is the quadratic equation, which has the general form ax² +bx +c = 0; where a, b, and c are constants and a is not equal 0. The solution for this type of equation can often be found by a method known as factoring.

Since the quadratic equation is the product of two first degree equations, it can be factored into these equations. For example, the product of the two expressions (x + 2)(x - 3) provides us with the quadratic expression x² - x - 6. The two expressions (x + 2) and (x - 3) are called factors of the quadratic expression x² - x - 6. By setting each factor of a quadratic equation equal to zero, solutions can be obtained. In this quadratic equation, the solutions are x = -2 and x = 3.

Finding the factors of a quadratic equation is not always easy. To solve this problem, the quadratic formula was invented so that any quadratic equation can be solved. The quadratic equation is stated as follows for the general equation ax² + bx + c = 0

To use the quadratic formula, numbers for a, b, and c are substituted into the equation, and the solutions for x are determined.