Deciding Which Method to Use when Solving Quadratic Equations When solving a quadratic equation, follow these steps (in this order) to decide on a method: Show
Example 1: Solve x2 + 4 = 4x First, put the equation in standard form so that we can try to solve it by factoring: x2 - 4x + 4 = 0 (x - 2)(x - 2) = 0 x - 2 = 0 | x - 2 = 0 x = 2 | x = 2 So the solution to this equation, found by factoring, is x = 2. Example 2: Solve (2x - 2)2 = -4 The side of the equation containing the variable (the left side) is a perfect square, so we'll take the square root of both sides to solve the equation. (2x - 2)2 = -4 2x - 2 = ± 2i 2x = 2 ± 2i x = 1 ± i Notice that the ± sign was inserted in the equation at the point that the square root was taken. Example 3: Solve x2 + 6x - 11 = 0 This equation is not factorable, and the side containing the variable is not a perfect square. But since the coefficient of the x2 is 1 and the coefficient of the x is even, completing the square will be an appropriate method. To find the number which needs to be added to both sides of the equation to complete the square, take the coefficient of the x term, divide it by 2, then square that number. In this problem, 6 ¸ 2 is 3, and 32 is 9, so we'll add 9 to both sides of the equation once we have isolated the variable terms. x2 + 6x - 11 = 0 x2 + 6x = 11 x2 + 6x +9 = 11 + 9 (x + 3)2 = 20 Example 4: Solve 2x2 - x + 5 = 0 This equation is not factorable, the left side is not a perfect square, and the coefficients of the x2 and x terms will not make completing the square convenient. That leaves the quadratic formula as the best method for solving this equation. We'll use a=2, b=-1, and c=5. An equation of the form ax2 + bx + c = 0, where a≠0 is called a quadratic equation. Answer: Follow the below steps to get the desired answer.Explanation: We have used four methods to solve quadratic equations:
Follow these steps in this order to choose a method for solving a quadratic equation:
Hence, with the help of the above steps, you can find the best method for solving a quadratic equation.How do you decide the best method to solve quadratic equation?Identify the most appropriate method to solve a quadratic equation.. Try Factoring first. If the quadratic factors easily, this method is very quick.. Try the Square Root Property next. If the equation fits the form or it can easily be solved by using the Square Root Property.. Use the Quadratic Formula.. What are the 4 methods of solving quadratic equations?The four methods of solving a quadratic equation are factoring, using the square roots, completing the square and the quadratic formula.
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