(x+4)^2-2x-5=(x-1)^2

Jasonbradley

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Jun 16, 2024

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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.