Question 64026: solve by factoring
x^2-10x=-16
Answer by praseenakos@yahoo.com(507)   (Show Source):
You can put this solution on YOUR website! QUESTION:
solve by factoring
x^2-10x=-16
ANSWER:
x^2-10x=-16
Add +16 on both sides of the equation
==> x^2-10x + 1`6= -16 + 16
==> x^2-10x + 16 = 0
This is a quadratic equation.
We can use quadratic fromula as well as factorisation method.
Factorisation method==>
x^2-10x + 16 = 0
First of all split the middle term.
For that find out two numbers whose sum is - 10 ( coefficient of x ) and whose product is +16 ( constant term )
Such two numbers are -8 and -2(( To get these numbers consider the factors of +16 , constant terms and try with different sign untill you get the numbers.)
Because,
-8 * -2 = -16 and -8 + ( -2 ) = -10
Now rewrite the given equation as follows,
x^2 - 8x - 2x + 16 = 0
Now group the terms as follows,
(x^2 - 8x ) - (2x - 16 ) = 0 ( when we put negative sign before the brackets, the sign inside the brackets will change)
Now take out common factor from each brackets.
==> x ( x - 8 ) - 2 ( x - 8 ) = 0
Again ( x - 8 ) is common in both terms, take it out.
==> ( x - 8 ) ( x - 2 ) = 0
Here we can take,
either ( x - 8 ) = 0 or ( x - 2 )= 0
If ( x - 8 ) = 0 ===> x = 8 and
If ( x - 2 ) = 0 ===> x = 2
So solution of given equation is,
x = 2 and
x = 8.
Hope you understood.
Regards.
praseenakos@yahoo.co.in
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