lesson 7 creating and solving quadratic equations

If it is there then you have to divide the whole equation first by the coefficient and then halve the coefficient of x and put it into the brackets. But remember, you only halve the coefficient of x and put it into the brackets only if there is no number before x^2 (coefficient of x^2). Where a is half the coefficient of x(the number before the x), as long a there is no coefficient of x^2. You want x^2 - 4x + (something) to be equal to (x-a)^2. (x-a)^2 is basically the format of the answer you want receive. Notice that now I could factorise the left hand side into (x - 2)^2

I want to factorise the left side of the equal sign, so I have to find a value for (something) which would allow me to factorise the left-hand side of the equation. Situations could vary, but this is the basic idea behind the procedure. Finally, you add 1 to both sides, taking into account that 4 could be positive OR negative. Next, you want to take the square root from both sides so that x-1 is equal to the positive or negative square root of 16 (positive or negative 4).

This will all give you the equation (x-1)^2=16. Because you´re taking this value away from the constant, you will add it to the other side of the equation (this might not make sense at first, but if the constant were on the variable side, you would be subtracting). In this case, you will add 1 because it perfectly factors out into (x-1)^2. Next, you want to add a value to the variable side so that when you factor that side, you will have a perfect square. Because there is a 3 in front of x^2, you will divide both sides by 3 to get x^2-2x=5. Next, you want to get rid of the coefficient before x^2 (a) because it won´t always be a perfect square. To do this, you will subtract 8 from both sides to get 3x^2-6x=15. To complete the square, first, you want to get the constant (c) on one side of the equation, and the variable(s) on the other side. You don´t need another video because I´m about to explain it to you! Say you have the equation 3x^2-6x+8=23.

Lesson 7 creating and solving quadratic equations