Final answer:
The solution of an equation is a value that makes the equation true, also known as the root. Quadratic equations can have up to two solutions due to the squared term, and solutions can be found through factoring, completing the square, or using the quadratic formula.
Step-by-step explanation:
The solution of an equation is any value that makes the equation true. This value is also known as the root or solution of the equation. In the context of quadratic equations, which are second-order polynomials, there can be up to two solutions because of the squared term. When solving these equations, you often employ methods such as factoring, completing the square, or using the quadratic formula to find the roots.
To solve for the unknown in any equation, begin by determining the knowns and unknowns. Identify an equation that expresses the unknown in terms of the knowns. If there is more than one unknown, multiple equations may be needed. Once the appropriate equation is identified, manipulate it algebraically to solve for the unknown.
In problems that involve quadratic equations, the standard form is ax^2 + bx + c = 0. As an example, consider the equation x^2 - 4x + 4 = 0. We can either factor it directly as (x - 2)^2 = 0, or use the quadratic formula. Factoring in this case is simpler, and it reveals that the solution is x = 2, which in this unique case is a repeated root, meaning both solutions are the same.