solving equation by using FOIL method

The FOIL Method is a process used in algebra to multiply two binomials. The lesson on the Distributive Property, explained how to multiply a monomial or a single term such as 7 by a binomial such as (4 + 9x).

But, what if there was a binomial instead of a single term outside of the parentheses? That is, what if a binomial was being multiplied by another binomial? An example of this is given in the problem.
Let's see an algebra question on this .

Question:-
Solve the equations by using foil method.

(y+1)(2y-3) = 25

Answer:-

Let's see how to solve equations using FOIL method.



(y+1)(2y-3) =25

2y²-3y+2y-3=25

2y²-y-3 = 25

2y²-y-3-25=0

2y²-y-28=0

2y²-8y+7y-28=0

2y(y-4)+7(y-4)=0

(y-4)(2y+7)=0

y-4=0 or 2y+7=0

y=4 or y= -7/2

y = 4 or -7/2 is the Answer

Completing the Square Method

Sometimes the roots of a quadratic equation cannot be obtained by simple factorization. So, a more general method is used. This method, which is based on the fact that any quadratic equation may be written in the form of (x+p)² = q, where p and q are real numbers, is known as completing the square method.

Question:-

Solve the equation by completing the square method.

2x²-7x+9=(x-3)(x+1)+3x

Answer:-

2x²-7x+9 = x²+x-3x-3+3x
-x²-x+3 -x²-x+3
---------------------------
x²-8x+12 = 0

now we solve this quadratic equation by completing the square method

x²-8x=-12

x²-8x+(8/2)²=(8/2)²-12

x²-8x+16 = 16-12

(x-4)² = 4

taking the square root on both sides, square root symbol looks like √ .

√(x-4)²= √4

x-4 = ±2

We also can use square root calculator to get these values.

x-4 = +2 or x-4 = -2

x=6 or x=2 is the answer

This equation have just one variable.similarly we can also work on linear equations in two variables

a word problem on equations

Topic:-Equations

solving equations is a mathematical statement, in symbols, that two things are exactly the same (or equivalent). Equations are written with an equal sign, as in

The equations above are examples of an equality: a proposition which states that two constants are equal. Equalities may be true or false.
Equations are often used to state the equality of two expressions containing one or more variables. In the reals we can say, for example, that for any given value .Here is a word problem on equations

Question:-

Solve

"Five times the difference of x
and 8 is lees than or equal to 20"

Answer:-

Let's bring it to a equation form.


Difference of x and 8 = x-8


Five times the difference of x  and 8 = 5(x-8)

less than or equal to 20 means  <=20             

Let's put together

5(x-8)<=20

Now let's go ahead and solve this


5(x-8)<=20

     5x - 40 < =20   Adding 40 on
        +40    +40   Both sides
  --------------------
         5x <= 60


Divde with 5 on both sides

         5x      60
        ---- <= ------
          5        5

          x< = 12

12 is the Answer.





 For more help you can reply me