%5E2-2x-5%3D(x-1)%5E2.jpeg "(x+4)^2-2x-5=(x-1)^2")
Solving the Equation: (x+4)^2 - 2x - 5 = (x-1)^2
This article explores the solution process for the equation (x+4)^2 - 2x - 5 = (x-1)^2. We will use algebraic manipulations to simplify the equation and find the value(s) of 'x' that satisfy it.
Step 1: Expanding the Squares
The first step is to expand the squared terms on both sides of the equation using the formula (a+b)^2 = a^2 + 2ab + b^2.
- Left Side: (x+4)^2 = x^2 + 8x + 16
- Right Side: (x-1)^2 = x^2 - 2x + 1
Substituting these expansions into the original equation, we get:
x^2 + 8x + 16 - 2x - 5 = x^2 - 2x + 1
Step 2: Simplifying the Equation
Next, we simplify the equation by combining like terms:
x^2 + 6x + 11 = x^2 - 2x + 1
Subtracting x^2 from both sides:
6x + 11 = -2x + 1
Adding 2x to both sides:
8x + 11 = 1
Subtracting 11 from both sides:
8x = -10
Step 3: Solving for x
Finally, we solve for 'x' by dividing both sides by 8:
x = -10 / 8
Simplifying the fraction, we get:
x = -5/4
Therefore, the solution to the equation (x+4)^2 - 2x - 5 = (x-1)^2 is x = -5/4.