But, I don't understand him.Complete square divided by 5 can give the remains 0,1 and 4, but not 3 like here.
The purpose of completing the square is to convert a quadratic expression into a perfect square trinomial. This allows us to easily solve quadratic equations and find the vertex of a parabola.
To complete the square, follow these steps:
1. Make sure the quadratic expression is in the form ax^2 + bx + c.
2. Take half of the coefficient of x (b) and square it.
3. Add this value to both sides of the equation.
4. Factor the perfect square trinomial on the left side.
5. Simplify and solve for x.
Adding the square of half the coefficient of x allows us to create a perfect square trinomial. This is necessary in order to factor the expression and solve the equation.
Yes, completing the square can be used for all quadratic equations. However, it is most useful for equations that cannot be easily solved by factoring or using the quadratic formula.
Yes, completing the square has many real-life applications, such as finding the minimum or maximum value of a quadratic function, predicting the trajectory of a projectile, and solving optimization problems in engineering and physics.