1. Stating the problem: We are given two equations involving variables $x$ and $x_2$: $$x + x \times x - x_2 = x$$ $$x + x \times x + x_2 = x$$ We need to analyze and solve these equations. 2. Simplify each equation by applying the order of operations (multiplication before addition/subtraction): For the first equation: $$x + x \times x - x_2 = x$$ $$x + x^2 - x_2 = x$$ For the second equation: $$x + x \times x + x_2 = x$$ $$x + x^2 + x_2 = x$$ 3. Rearrange each equation to isolate $x_2$: From the first equation: $$x + x^2 - x_2 = x \implies x^2 - x_2 = 0 \implies x_2 = x^2$$ From the second equation: $$x + x^2 + x_2 = x \implies x^2 + x_2 = 0 \implies x_2 = -x^2$$ 4. Interpretation: The two equations imply contradictory values for $x_2$ unless $x^2 = 0$. 5. Solve for $x$ when $x^2 = 0$: $$x^2 = 0 \implies x = 0$$ 6. Substitute $x=0$ back into the expressions for $x_2$: $$x_2 = x^2 = 0$$ $$x_2 = -x^2 = 0$$ Both equations are satisfied when $x=0$ and $x_2=0$. Final answer: The only solution that satisfies both equations simultaneously is $$x = 0, \quad x_2 = 0$$