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For any of the following methods, first make sure that all terms of the equation are on the left of the equal sign; on the right, there should only be a zero. Thus, for example,
x2 - 5x = 10
becomes:
x2 - 5x - 10 = 0
The methods commonly used are:
1) Factor the polynomial. Sometimes this can be done easily; but if this is too difficult, use one of the other methods below.
2) Complete the square. Add a constant term to both sides of the equation, such that the polynomial on the left becomes a perfect square.
3) Use the quadratic formula. This is usually the simplest method, if you can't find an obvious factorization quickly.
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What is the quadratic formula used for?
The quadratic formula is used all the time to solve quadratic equations, often when the factors are fractions or decimals but sometimes as the first choice of solving method. The quadratic formula is sometimes faster than completing the square or any other factoring methods. Quadratic formula find: -x-intercept -where the parabola cross the x-axis -roots -solutions
What is a method used to solve systems of equations in which the solution is the point where the lines intersect?
there are three methods: combination, substitution and decomposition.
What are 2 symbolic techniques used to solve linear equations and which is better?
There are more than two methods, and of these, matrix inversion is probably the easiest for solving systems of linear equations in several unknowns.
How do you solve quadratic equations by factoring?
There is a new method, called Diagonal Sum Method, that quickly and directly give the 2 roots without having to factor the equation. The innovative concept of this method is finding 2 fractions knowing their sum (-b/a) and their product (c/a). It is fast, convenient and is applicable to any quadratic equation in standard form ax^2 + bx + c = 0, whenever it can be factored. If it fails to find answer, then the equation is not factorable, and consequently, the quadratic formula must be used. So, I advise you to proceed solving any quadratic equation in 2 steps. First, find out if the equation can be factored? How?. Use this new method to solve it. It usually takes fewer than 3 trials. If its fails then use the quadratic formula to solve it in the second step. See book titled:" New methods for solving quadratic equations and inequalities" (Trafford Publishing 2009)
What methods can be used to solve a system of equations?
The answer depends on the nature of the equations. For a system of linear equations, the [generalised] inverse matrix is probably simplest. For a mix of linear and non-linear equations the options include substitution, graphic methods, iteration and numerical approximations. The latter includes trail and improvement. Then there are multi-dimensional versions of "steepest descent".
