hi guys it's me teacher going in today's video we will talk about solving quadratic equations by completing the square so in our previous two videos we talked about solving quadratic equations by factoring and extracting the square roots so i will try to put the links of those videos out in description box so without further ado let's do this topic what we have here is x squared plus 6x minus 2 is equal to zero so there are different ways on how to solve quadratic equations perro a common lingua gamma students that are solving equations i by factoring like this one x squared plus six x minus two is equal to zero is difficult to factor out that's why meron tai another way or method which is completing the square so i'm completing the square and in case one nothing if the coefficient here is one okay if the coefficient of your quadratic term x squared is 1. first step is to transpose this negative term or this negative 2 or the constant to the other side of the equation so what will happen is that we will transpose this to the other side so what will happen is that we have x squared plus 6x is equal to from negative when you transpose it it will change change the sign it will become positive two so as you can see i have provided here a space where in we need to find a third term here that will make this whole expression uh as a perfect square trinomial so again we will put plus blank here so how do we get the third term that will make this expression a perfect square trinomial we have the pattern or the standard form ax squared plus bx plus c is equal to zero what you need to do is to get the value of b or the coefficient b and then divide it by 2 then square your quotient here in your x squared plus 6 this is the value of b 6. so what we have here is six divided by two squared simplifying that and six divided by two is three squared that is nine so this is now the third term so we have plus nine here and plus nine also to the other side of the equation so as you can see this expression is already a perfect square trinomial next step now then is to express this perfect square trinomial into a square of binomial so that is x plus 3 squared is equal to 2 plus 9 which is equal to 11. now there's a question sir how do you get x plus 3 squared simply on the mind get the square root of your first term x squared that is x get the square root of your third term which is 9 that is equal to 3 and then copy this sign of your middle term so after that we need to use extracting the square roots get the square root of this and get the square root of this and remember when you're getting the square root of a number in quadratic equations you need to put positive and negative here so for this part all you need to do is to cancel out the radical sign and exponent 2. so what we have here is simply x plus 3 is equal to positive negative square root of 11 so it remains square root of 11 because 11 is not a perfect square next step is to isolate the variable x meaning we need to remove positive 3 and transpose it to the other side of the equation so that is x is equal to positive negative square root of 11 from positive it will become negative or minus 3. so in this case since we already isolated the variable x we can now start solving for the first and second value of x so we will name it as x sub 1. and x sub 2. for x sub 1 we will use first the positive square root of 11 or simply square root of 11 then minus 3. so dito uh there's no need to simplify this one is already the final answer so we can decide that this one is your answer so can we interchange negative 3 and 11 and square root of 11 yes you can also express your answer as negative 3 plus the square root of 11. and for your x sub 2 since we are done using the positive square root of 11 we will now use the negative square root of 11 and then copy negative 3 or minus 3 and this is now the value or the second root of the given quadratic equation x squared plus 6x minus two is equal to zero so i hope guys another example nathan for number one and we will upload a video where in we will discuss the part two of this given topic wherein the coefficient of your first term is not one that is greater than one so if you're new to my channel don't forget to like and subscribe but hit the bell button for you to be updated certain latest uploads again it's meet urgon bye-bye