Completing Square Method to Solve Quadratic Equations | Concept Clarification | Solve in Easy way

Completing Square Method to Solve Quadratic Equations | Concept Clarification | Solve in Easy way

In this video, Completing Square Method to Solve Quadratic Equations are Explained.
Questions Covered are like
2x²-7x+3

One must watch this lecture. This method explained in the video is very helpful for making maths calculation easy specially in competitive exams.

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For quadratic equations that cannot be solved by factorising, we use a method which can solve ALL quadratic equations called completing the square. We use this later when studying circles in plane analytic geometry.

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Completing Square Method of Quadratic Equations

When solving a quadratic equation, follow these steps (in this order) to decide on a method:

Try first to solve the equation by factoring. Be sure that your equation is in standard form (ax2+bx+c=0) before you start your factoring attempt. Don't waste a lot of time trying to factor your equation; if you can't get it factored in less than 60 seconds, move on to another method.
Next, look at the side of the equation containing the variable. Is that side a perfect square? If it is, then you can solve the equation by taking the square root of both sides of the equation. Don't forget to include a ± sign in your equation once you have taken the square root.
Next, if the coefficient of the squared term is 1 and the coefficient of the linear (middle) term is even, completing the square is a good method to use.
Finally, the quadratic formula will work on any quadratic equation. However, if using the formula results in awkwardly large numbers under the radical sign, another method of solving may be a better choice.
Now we'll look at some equations and think about the most appropriate method for solving them.


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.

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[sushantdahal]

Great job Man.

I believe you're the only one to mention the use of the following formulas:

(A+B)^2 = A^2 + 2AB+ B^2
(A-B)^2 = A^2 - 2AB + B^2

Since above formulas are the only key to make complete square.

Most of the youtubians don't even mention above formulas, they simply skip them and write directly.

Good Job!

[totalgamings]

Best explanation🎉🎉, guyys who are new here can blibly trust on this man

[FarhanAli-dupt]

You also are a good teacher ❤
Respect from Pakistan

[newideas]

Thanks for this concept sir 👍👍
I hope you may got more success than it { YouTube }. .in your life.. 😊😊

[AdityaRajput-xdjm]

means a lot, this video is fabulous to teaching the concept like this

[manafkhan]

You r just amazing sir 👏 ❤ Thank-you sir 🥰

[nikxnj_]

This method is deleted or not in cbse class 10th 2022-24?

[TanishBisht-yj]

your explanation as well as writing is superb sir, keep going

[Nep.kishan]

Thank you so much sir, I went very weakness in quadric equation square method but now I 😮😮 am very strong in I this you 🙏🙏💪🙏

[United-States_Federation]

don't do labour
use Descriminate method.😊

[vishalkumargaur]

Sir mainus 3by2 ke bagal m 7by4 q likhe hai
Both side multiply q hoga

[Yashpal]

Sir muje confusion ho rhi thi ki x2 jab negative ho to kese PTA kare formula uska solution hai ki x2 ko +1 bna lo or x ka sign dhek lo😊

[AbuMuzamil-kb]

Sir G if we multiply 3 then what happen🙏🙏🙏

[syedsharfuddin]

Hello sir how are you

Sir I request you make of class 12th integration chapter video i hope you will make the chapter of integration

[SajidaAzimi-kxir]

Sir agar x k coefficient one hi ho to kasy solve kary ga

[VIVEKRATHORE-go]

1st step is taking the equation in standard form