(x-5)%3D-1.jpeg "(x-3)(x-5)=-1")
Solving the Equation (x-3)(x-5) = -1
This equation presents a quadratic equation in factored form. Let's break down how to solve it.
1. Expand the Equation
First, we need to expand the left side of the equation:
(x-3)(x-5) = -1 x² - 8x + 15 = -1
2. Move Constant Term to the Left Side
To get a standard quadratic form, move the constant term from the right side to the left:
x² - 8x + 15 + 1 = 0 x² - 8x + 16 = 0
3. Factor the Quadratic Expression
The left side of the equation is now a perfect square trinomial:
(x - 4)² = 0
4. Solve for x
Take the square root of both sides:
x - 4 = 0
Finally, solve for x:
x = 4
Solution
Therefore, the solution to the equation (x-3)(x-5) = -1 is x = 4.
This means that when you substitute x = 4 back into the original equation, it will be true.