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A quadratic equation
(X-4)^2=55
(x+8)^2=105
In the special case when a =1, the factoring method results in finding 2 NUMBERS knowing their sum and their product. The process is simple. However, when the constants a, b, c are large numbers, and contain themselves many factors, then the factoring method becomes complicated and takes long time in the process. For examples, solving these equations by the factoring method will take lot of time because of the high number of permutations: (6x^2 - 11x - 35 = 0) ; (45x^2 + 74x - 55 = 0) ; (45x^2 - 152x - 36 = 0); (12x^2 + 5x - 72 = 0) There is a new method, called Diagonal Sum Method, that can quickly and directly give the 2 roots, WITHOUT HAVING TO FACTOR THE EQUATION. The innovative concept of the new method is finding 2 FRACTIONS knowing their sum (-b/a) and their product (c/a). It is faster, more convenient than the factoring method since it requires fewer permutations by using the rule of signs for real roots. It is applicable whenever the equation can be factored. So, I advise you to proceed solving any quadratic equation in 2 steps. First step, use the Diagonal Sum method to solve it. It usually takes fewer than 3 trials. If it fails, then the quadratic formula must be used in second step. See book title:" New method for solving quadratic equations and inequalities" (Trafford Publishing 2009)
That's the "solution" to the equation described by the sentence.
A quadratic equation
(X-4)^2=55
(x+8)^2=105
I guess you mean the standard quadratic equation, of the form ax^2 + bx + c = 0.There are three main algebraic methods, namely: * Factoring * Completing the square * Using the quadratic formula Since you want five, here are a few more, but they are usually not very convenient to use for this particular type of equation: * Trial and error * Graphic the equation * Diverse iterative methods, such as Newton's method, etc.
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The vertex form of this function.X2 + 22X = 31Halve the linear term ( 22 ) square it and add it to both sides.X2 + 22X + 121 = 31 + 121Factor the left side of this equation and gather terms on the right side.(X + 11)2 = 152(X + 11)2 - 152 = 0===================vertex form of this function(- 11, - 152 )===========Vertex
The three basic rules for factoring are as followed:The number must be a whole numberEnd results must be the basis of numbersCannot be less than zero
after completing xam we will get the results.................
Integration results in an equation which gives the area under the original equation between the bounds. Derivation results in an equation which gives the slope of the original line at any point.
Successful
Yes, however not all quadratic equations can easily be solved by factoring, sometimes you can factor and sometimes it is easier to use the quadratic formula. Example: x2 + 4x + 4 This can be easily factored to (x + 2)(x +2) Therefore the answer is -2 by setting x +2 = 0 and solving for x This can be done using the quadratic equation and you would get the same results, however, it was much faster to factor instead.
Two equations are equal when the result of the functions of the numbers and variables of one equation match the results of the other equation.