Solving for a in the Quadratic Equation (x+2)^2=a Given x=1
Quadratic equations are one of the most fundamental concepts in mathematics. They are used to solve a wide range of problems and are essential in various fields of study, including physics, engineering, and economics. One of the most common types of quadratic equations is the (x+2)^2=a equation, where x is an unknown variable and a is a given constant. In this blog post, we will explore how to solve for a in the quadratic equation (x+2)^2=a, given x=1.
First, let us recall the standard form of a quadratic equation: ax^2+bx+c = 0. We can rewrite the given equation (x+2)^2=a as x^2+4x+4=a by expanding the square. Since we know that x=1, we can substitute it into the equation to get 1^2+4(1)+4=a, which simplifies to 9=a.
Therefore, the value of a that solves the equation (x+2)^2=a when x=1 is 9. It is that simple!
In conclusion, solving for a in the quadratic equation (x+2)^2=a when x=1 is a straightforward process. By substituting x=1 into the equation and solving for a, we find that a=9. This kind of exercise is a great way to practice your algebraic skills, and it reinforces the concept of quadratic equations. With practice, you can tackle more complex problems and master this critical mathematical tool.