平方完成裏ワザ: Tips And Tricks For Solving Quadratic Equations
Terbaik japan website . sedang mencari japan in diweb ini.
小閣樓摺疊樓梯怎麼樣？市場價格是多少？ 每日頭條 from kknews.cc
Introduction
If you're struggling with solving quadratic equations, you're not alone! Many students find this topic challenging, but with the right tips and tricks, you can master it. In this article, we'll be discussing the "平方完成裏ワザ," or the hidden technique for completing the square.
What is Completing the Square?
Completing the square is a technique used to solve quadratic equations of the form ax^2 + bx + c = 0. The goal is to rewrite the equation in the form (x + p)^2 = q, where p and q are constants. This makes it easier to solve for x. However, completing the square can be time-consuming and difficult, especially if the coefficients are not simple numbers.
The Hidden Technique
The "平方完成裏ワザ" is a shortcut for completing the square. Instead of using the traditional method, you can use this technique to quickly and easily rewrite the equation in the desired form. Here's how it works: 1. Divide both sides of the equation by a: ax^2 + bx + c = 0 becomes x^2 + (b/a)x + (c/a) = 0. 2. Subtract (c/a) from both sides: x^2 + (b/a)x = -(c/a). 3. Add (b/2a)^2 to both sides: x^2 + (b/a)x + (b/2a)^2 = (b/2a)^2 - (c/a). 4. Rewrite the left side as (x + b/2a)^2: (x + b/2a)^2 = (b/2a)^2 - (c/a). 5. Take the square root of both sides: x + b/2a = ±√((b/2a)^2 - (c/a)). 6. Solve for x: x = (-b ± √(b^2 - 4ac))/2a.
Examples
Let's try using the "平方完成裏ワザ" to solve some quadratic equations. Example 1: x^2 + 6x + 8 = 0 1. Divide by 1: x^2 + 6x + 8 = 0 becomes x^2 + 6x + 8 = 0. 2. Subtract 8: x^2 + 6x = -8. 3. Add 9: x^2 + 6x + 9 = 1. 4. Rewrite as (x + 3)^2: (x + 3)^2 = 1. 5. Take the square root: x + 3 = ±1. 6. Solve for x: x = -4 or -2. Example 2: 2x^2 - 4x + 1 = 0 1. Divide by 2: 2x^2 - 4x + 1 = 0 becomes x^2 - 2x + 1/2 = 0. 2. Subtract 1/2: x^2 - 2x = -1/2. 3. Add 1/4: x^2 - 2x + 1/4 = 1/4. 4. Rewrite as (x - 1)^2: (x - 1)^2 = 1/4. 5. Take the square root: x - 1 = ±1/2. 6. Solve for x: x = 3/2 or 1/2.
Conclusion
The "平方完成裏ワザ" is a useful technique for solving quadratic equations. By using this shortcut, you can save time and avoid making mistakes. Remember to practice solving equations using this technique, and you'll be a pro in no time!
