Question

Tell me more about the method of "completing the square".

Answer 1

Completing the square is a method used to solve quadratic equations in the form of ax^2 + bx + c = 0, where a, b, and c are constants. The method involves manipulating the equation to create a perfect square trinomial, which can then be easily solved using square roots.To complete the square, follow these steps:1. Move the constant term (c) to the right side of the equation, leaving only the x^2 and x terms on the left side.2. Divide both sides of the equation by the coefficient of x^2 (a) to make the coefficient of x^2 equal to 1.3. Take half of the coefficient of x (b/2) and square it (b/2)^2.4. Add this value to both sides of the equation.5. On the left side, write the expression as a perfect square trinomial by factoring (x + b/2)^2.6. Take the square root of both sides of the equation and solve for x.For example, to solve the equation x^2 + 6x + 5 = 0 using completing the square:1. Move the constant term to the right side: x^2 +