%5E2%3D1.jpeg "(a+5)^2=1")
(a+5)^2 = 1: Solving the Quadratic Equation
In this article, we will explore the solution to the quadratic equation (a+5)^2 = 1. This equation is a classic example of a quadratic equation, and solving it requires a solid understanding of algebraic manipulations and properties of squares.
Expanding the Equation
To start, let's expand the equation using the distributive property of multiplication over addition:
(a+5)^2 = (a+5)(a+5)
= a^2 + 10a + 25
Rearranging the Equation
Now, let's rearrange the equation to put it in the standard form of a quadratic equation:
a^2 + 10a + 24 = 0
Factoring the Equation
Can we factor the quadratic expression? Let's try:
a^2 + 10a + 24 = (a + 4)(a + 6) = 0
Solving for a
Now that we have factored the equation, we can solve for a by setting each factor equal to 0:
a + 4 = 0 or a + 6 = 0
Solving for a, we get:
a = -4 or a = -6
Conclusion
Therefore, the solutions to the equation (a+5)^2 = 1 are a = -4 and a = -6. These values of a satisfy the original equation, and we have successfully solved the quadratic equation!
