Question

Katie performed the steps shown below to solve a quadratic equation using the method of completing the square. X^2 - 12 = 2 -4x + 7y = 1, multiply each term x - 12y = 2 by -4 and add it to the other equation

Answer 1

Completing the square is a method used to solve quadratic equations by turning them into a perfect square trinomial. When this is not practical, the quadratic formula provides a reliable alternative for solving any quadratic equation.

Step-by-step explanation:

The solution to a quadratic equation can often be found by completing the square, which involves creating a perfect square trinomial from a quadratic expression. In some cases, it is more efficient than using the quadratic formula, especially if the quadratic can be easily converted into a perfect square.

For instance, in an equation like x² + bx + c = 0, we can turn the left side into a perfect square by adding and subtracting the square of half of the coefficient of x ((b/2)²). However, if the equation is not easily transformed into a perfect square, or if it has complicated coefficients, using the quadratic formula might be the best approach. The quadratic formula is given by (-b ± √(b² - 4ac)) / (2a), and it solves any quadratic equation, regardless of whether or not the equation is a perfect square.