solving a quadratic equation needing simplification

SOLVING A QUADRATIC EQUATION NEEDING SIMPLIFICATION HOW TO
SOLVING A QUADRATIC EQUATION NEEDING SIMPLIFICATION TRIAL

Need to understand even what it's all about. Video after that I'll prove the quadratic formula usingĬompleting the square. That this will work for any quadratic equation, and it'sĪctually the basis for the quadratic formula. You a technique called completing the square. Sorry for the large number of words used to answer your question. Sal uses (x - a)^2 simply to tell this is the format of the factorised form of : 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. = (5 + x)(5 - x) Ĭlick here to find more information on quadratic equations.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. This is because a² - b² = (a + b)(a - b). If you are asked to factorise an expression which is one square number minus another, you can factorise it immediately.

SOLVING A QUADRATIC EQUATION NEEDING SIMPLIFICATION TRIAL

Unfortunately, the only other method of factorising is by trial and error. It is worth studying these examples further if you do not understand what is happening. Once you work out what is going on, this method makes factorising any expression easy. We need to split the 2x into two numbers which multiply to give -8. Now, make the last two expressions look like the expression in the bracket: The first two terms, 12y² and -18y both divide by 6y, so 'take out' this factor of 6y.Ħy(2y - 3) - 2y + 3 One systematic method, however, is as follows: There is no simple method of factorising a quadratic expression, but with a little practise it becomes easier.

SOLVING A QUADRATIC EQUATION NEEDING SIMPLIFICATION HOW TO

This video shows you how to solve a quadratic equation by factoring. So if you were asked to factorise x² + x, since x goes into both terms, you would write x(x + 1). The first step of factorising an expression is to 'take out' any common factors which the terms have. This is an important way of solving quadratic equations. 2 x( x + 3) = 2x² + 6x ).įor an expression of the form (a + b)(c + d), the expanded version is ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.įactorising is the reverse of expanding brackets, so it is, for example, putting 2x² + x - 3 into the form (2x + 3)(x - 1). This section shows you how to factorise and includes examples, sample questions and videos.īrackets should be expanded in the following ways:įor an expression of the form a(b + c), the expanded version is ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket (e.g.

Solving a quadratic equation needing simplification