Solve x²-(x+4)²=40: Perfect Square Binomial Challenge

To solve the equation $x^2 - (x+4)^2 = 40$, follow these steps:

• Step 1: Expand the square $(x+4)^2$.
• Step 2: Substitute the expansion into the original equation.
• Step 3: Simplify the resulting expression.
• Step 4: Solve the simplified equation for $x$.

Let's work through each step:

Step 1: Expand $(x+4)^2$:
$(x+4)^2 = x^2 + 8x + 16$

Step 2: Substitute this into the original equation:
$x^2 - (x^2 + 8x + 16) = 40$

Step 3: Simplify the equation:
$x^2 - x^2 - 8x - 16 = 40$

Upon simplification, the equation becomes:
$-8x - 16 = 40$

Step 4: Solve for $x$:
Add 16 to both sides:
$-8x = 56$

Divide by $-8$:
$x = -\frac{56}{8} = -7$

Therefore, the solution to the problem is $x = -7$.