What Is the Solution to the Equation Below?
In mathematics, an equation is a statement that two expressions are equal. The solution to an equation is the value of the variable that makes the equation true.
To find the solution to an equation, we can use a variety of methods. One common method is to solve for the variable by isolating it on one side of the equation. To do this, we can use the following steps:
- Subtract or add any constants to both sides of the equation.
- Multiply or divide both sides of the equation by the same number, as long as the number does not equal zero.
- Simplify both sides of the equation.
For example, let’s say we have the equation below:
x + 2 = 5 To solve for x, we can subtract 2 from both sides of the equation:
x + 2 - 2 = 5 - 2 x = 3 Therefore, the solution to the equation x + 2 = 5 is x = 3.
Another common method for solving equations is to use the quadratic formula. The quadratic formula is a formula that can be used to solve any quadratic equation, which is an equation of the form ax^2 + bx + c = 0. The quadratic formula is as follows:
x = (-b ± √(b^2 - 4ac)) / 2a where a, b, and c are the coefficients of the quadratic equation.
For example, let’s say we have the quadratic equation below:
x^2 - 5x + 6 = 0 To solve for x, we can use the quadratic formula:
x = (5 ± √(-5^2 - 4 * 1 * 6)) / 2 * 1 x = (5 ± √(25 - 24)) / 2 x = (5 ± 1) / 2 x = 3 or 2 Therefore, the solutions to the equation x^2 – 5x + 6 = 0 are x = 3 and x = 2.
Related Questions
Here are some related questions that can be asked about the solution to an equation:
- What is the domain of the solution?
- What is the range of the solution?
- Is the solution unique?
- Are there any extraneous solutions?
The domain of a solution is the set of all possible values of the variable that make the equation true. The range of a solution is the set of all possible values of the expression on the right side of the equation.
A solution is unique if there is only one value of the variable that makes the equation true. Extraneous solutions are solutions that are not in the domain of the equation.
For example, let’s consider the equation below:
x^2 + 4 = 0 The solution to this equation is x = -2. The domain of this equation is all real numbers. The range of this equation is all non-negative real numbers.
The equation x^2 + 4 = 0 also has the solution x = 2. However, this solution is extraneous because it is not in the domain of the equation.
I hope this article has been helpful.