(a%2B3)%3D8.jpeg "(a-4)(a+3)=8")
Solving the Equation (a - 4)(a + 3) = 8
This equation involves a quadratic expression and we need to solve for the unknown variable 'a'. Let's break down the steps to find the solution.
1. Expand the Equation
First, expand the left side of the equation by multiplying the two factors:
(a - 4)(a + 3) = a² - a - 12
Now, the equation becomes:
a² - a - 12 = 8
2. Move Constant Term to the Left Side
To make it easier to solve, move the constant term (8) to the left side of the equation:
a² - a - 12 - 8 = 0
This simplifies to:
a² - a - 20 = 0
3. Factor the Quadratic Expression
Now we need to factor the quadratic expression on the left side:
(a - 5)(a + 4) = 0
4. Solve for 'a'
For the product of two factors to be zero, at least one of the factors must be zero. So, we have two possible solutions:
- a - 5 = 0 which leads to a = 5
- a + 4 = 0 which leads to a = -4
Conclusion
Therefore, the solutions to the equation (a - 4)(a + 3) = 8 are a = 5 and a = -4.