1. The problem is to solve a quadratic equation using the squaring method. 2. Suppose the quadratic equation is $ax^2 + bx + c = 0$. 3. First, isolate the square root term if the equation involves a square root, or rewrite the equation to express one side as a square. 4. For example, if the equation is $\sqrt{x} = k$, square both sides to get $x = k^2$. 5. If the equation is $x^2 + bx = -c$, complete the square by adding $\left(\frac{b}{2}\right)^2$ to both sides: $$x^2 + bx + \left(\frac{b}{2}\right)^2 = -c + \left(\frac{b}{2}\right)^2$$ 6. This gives $\left(x + \frac{b}{2}\right)^2 = \left(\frac{b}{2}\right)^2 - c$. 7. Now, take the square root of both sides: $$x + \frac{b}{2} = \pm \sqrt{\left(\frac{b}{2}\right)^2 - c}$$ 8. Finally, solve for $x$: $$x = -\frac{b}{2} \pm \sqrt{\left(\frac{b}{2}\right)^2 - c}$$ 9. This is the solution to the quadratic equation by the squaring method. 10. Always check for extraneous solutions by substituting back into the original equation.