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Factoring a quadratic equation is the opposite of expanding an equation. FOILing (first, outer, inner, last) is the common technique used to do this.
Example of foiling: (x + 4) (x + 1) = x2 + 1x + 4x + 4, which simplifies to x2 + 5x + 4.
Because factoring is the opposite of foiling we are going to move backwards, but in a different way. The solution to a factoring problem is the beginning of a foiling problem.
Factoring Example:
x2 + 5x + 4 = 0
NOTE: your equation might not be equal to anything. It may appear as x2 + 5x + 4. In that case do the following steps as they appear but leave out the "= 0" from your answer because it's not there. Also do not do STEP 4 if it's not equal to zero.
STEP 1. x2 is equal to x multiplied by x, so separate the x's.
(x ) (x ) = 0
STEP 2. Look at the last number in the quadratic equation (4), take the multiples of that number (4) and see which set of multiples adds up the the middle number (5).
Multiples of 4: 2 and 2 (2 x 2 = 4), 4 and 1 (4 x 1 = 4).
2 + 2 = 4, 4 is not the middle # (5). 4 + 1 = 5!! Use 4 and 1.
(x 4) (x 1) = 0
STEP 3. Look at the sign (positive or negative) of the middle number you are trying to add up to. The signs of the 4 and 1 must fit too.
Middle number is a POSITIVE 5.
postive 4 + positive 1 = positive 5 <--- that's right!
but negative 4 + positive 1 = negative 3 <--- that's wrong!
negative 4 + negative 1 = negative 5 <--- that's wrong!
positive 4 + negative 1 = positive 3 <--- that's wrong!
(x + 4) (x + 1) << GRAND ANSWER!!! (unless equal to 0)
(x + 4) (x + 1) = 0
STEP 4. Sometimes the equation will not be set equal to anything. If that's the case, then (x + 4) (x + 1) is the correct answer. If it is set equal to zero then take each part of the new equation equal to zero and solve for x.
x+4 = 0 >> subtract 4 from both sides and you get x = -4
and
x + 1 = 0 >> subtract 1 from both sides and you get x = -1
x = -4 or x = -1 << GRAND ANSWER!!! :)
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How do you solve simultaneous quadratic equations?
Graphically might be the simplest answer.
What are the pros and cons of the quadratic equation?
Pros: There are many real life situations in which the relationship between two variables is quadratic rather than linear. So to solve these situations quadratic equations are necessary. There is a simple equation to solve any quadratic equation. Cons: Pupils who are still studying basic mathematics will not be told how to solve quadratic equations in some circumstances - when the solutions lie in the Complex field.
How do you use a graphing calculator to solve quadratic equations?
Graph the equation then find the x intercepts.
What is the graph of a quadratic formula?
In general, quadratic equations have graphs that are parabolas. The quadratic formula tells us how to find the roots of a quadratic equations. If those roots are real, they are the x intercepts of the parabola.
How do you solve a biquadratic equation?
Equations of the form z^4+az^2+a_0 are known as biquadratic equations. They are quartic equations. In general they can be solved by reducing them to a quadratic equation where x=z^2 is the variable. Then you can use the quadratic formula or factor. So plugging in x to the biquadratic giives us x^2+ax+a_0.
What does quadratic equations using the factoring method means?
It means you are required to "solve" a quadratic equation by factorising the quadratic equation into two binomial expressions. Solving means to find the value(s) of the variable for which the expression equals zero.
In mathematics how does one use the quadratic formula?
The Quadratic formula in mathematics is used to solve quadratic equations in algebra. The simplest way to solve these equations is to set each of the factors to zero and then solve each factor separately.
How do you solve quadratic equations by graphing?
josh hutcherson
How did the Babylonians solve quadratic equations?
1+1=2
How do you solve simultaneous quadratic equations?
Graphically might be the simplest answer.
What is the quadratic formula for?
The quadratic formula is used to solve the quadratic equation. Many equations in which the variable is squared can be written as a quadratic equation, and then solved with the quadratic formula.
What is the quadratic equation used for?
It is used to solve quadratic equations that cannot be factored. Usually you would factor a quadratic equation, identify the critical values and solve, but when you cannot factor you utilize the quadratic equation.
Why do you use square roots to solve quadratic equations?
Because it's part of the quadratic equation formula in finding the roots of a quadratic equation.
What is a great website to use for quadratic equations?
Wolfram Alpha can solve not just quadratic equations, but all sorts of equations. Note that in this particular website, you can see the solution for free, but you need a paid subscription to show the steps. I am sure there are other websites that can help you as well; you may want to try a Web search for "quadratic equation", for example. On the other hand, you should definitely learn to solve quadratic equations on your own.
What are the pros and cons of the quadratic equation?
Pros: There are many real life situations in which the relationship between two variables is quadratic rather than linear. So to solve these situations quadratic equations are necessary. There is a simple equation to solve any quadratic equation. Cons: Pupils who are still studying basic mathematics will not be told how to solve quadratic equations in some circumstances - when the solutions lie in the Complex field.
How does the zero product rule help you solve quadratic equations?
Factor it! Set each equal to zero! Solve
What is the difference between a linear quadratic and a quadratic quadratic?
There is no quadratic equation that is 'linear'. There are linear equations and quadratic equations. Linear equations are equations in which the degree of the variable is 1, and quadratic equations are those equations in which the degree of the variable is 2.
