(x+9)(x-3)=(x+1)^2

2 min read Jun 17, 2024

Solving the Equation: (x+9)(x-3) = (x+1)^2

This article will guide you through solving the equation (x+9)(x-3) = (x+1)^2. We will use algebraic manipulation to isolate the variable 'x' and find its value.

Expanding the Equation

First, we need to expand both sides of the equation:

Left side: (x+9)(x-3) = x² + 6x - 27
Right side: (x+1)² = x² + 2x + 1

Now the equation becomes: x² + 6x - 27 = x² + 2x + 1

Simplifying the Equation

Next, we can simplify the equation by combining like terms:

Subtract x² from both sides: 6x - 27 = 2x + 1
Subtract 2x from both sides: 4x - 27 = 1
Add 27 to both sides: 4x = 28

Isolating the Variable

Finally, we isolate 'x' by dividing both sides by 4:

Divide both sides by 4: x = 7

Solution

Therefore, the solution to the equation (x+9)(x-3) = (x+1)² is x = 7.

Verification

We can verify our answer by substituting x = 7 back into the original equation:

Left side: (7+9)(7-3) = 16 * 4 = 64
Right side: (7+1)² = 8² = 64

Since both sides equal 64, our solution x = 7 is correct.