To solve for $x$, we need to analyze the triangle from the given image. It looks like we have a right-angled triangle with some side lengths expressed in terms of $x$.

From the image:

• The base of the triangle is labeled as $x + 2$.
• The height is labeled as $x - 2$.
• The hypotenuse is labeled as $x$.

We can apply the Pythagorean theorem to solve for $x$, which states:

$a^2 + b^2 = c^2$

Where $a$ and $b$ are the lengths of the legs, and $c$ is the length of the hypotenuse. Here, $a = x + 2$, $b = x - 2$, and $c = x$.

Using the Pythagorean theorem:

$(x + 2)^2 + (x - 2)^2 = x^2$

Let's expand and simplify this equation to solve for $x$. sympy import symbols, Eq, expand, solve

Define the variable

x = symbols('x')

Define the equation using Pythagorean theorem

equation = Eq((x + 2)**2 + (x - 2)2, x2)

Expand the equation

expanded_equation = expand(equation)

Solve the equation

solutions = solve(expanded_equation, x) solutionsThe solutions to the equation are complex numbers: $-2\sqrt{2}i$ and $2\sqrt{2}i$, where $i$ is the imaginary unit.

Given that the lengths of the sides of a triangle cannot be imaginary, it suggests that there might be an error or inconsistency with the problem setup or the given expressions for the side lengths. Could you please confirm if the values or relationships provided for the triangle are correct, or if there are any other details that might help clarify the situation?