SOLUTION: 24 less than the square of a number is five times the number. find all such numbers.

Question 63559: 24 less than the square of a number is five times the number. find all such numbers.
Found 2 solutions by stanbon, praseenakos@yahoo.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
24 less than the square of a number is five times the number. find all such numbers
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Let the number be "x".
EQUATION:
x^2-24=5x
x^2-5x-24=0
(x-8)(x+3)=0
x=9 or x=-3
Cheers,
Stan H.
Answer by praseenakos@yahoo.com(507) (Show Source): You can put this solution on YOUR website!
QUESTION:
24 less than the square of a number is five times the number. find all such numbers.
ANSWER:
Suppose the number be, " x "
Square of that number = x^2

24 less than the square of the number = x^2 -24
Five times the number = 5x

Now,24 less than the square of a number = five times the number

==> x^2 -24 = 5x

==> x^2 -24 - 5x = 5x -5x ( subtract 5x from both sides)

==> x^2- 5x -24 = 0

This is a quadratic equation.

We can solve it using splitting the middle term or using quadratic formula.

Method 1:

x^2- 8x+3x -24 = 0 (split the middle term so that sum of the numbers is -5 and their product is -24

(x^2- 8x)+(3x -24) = 0 ( group the terms)

x(x-8) + 3(x-8) = 0 ( take out common terms from each group.)

==>( x-8)(x+3)= 0 (since x-8 is common in both terrms, again take it out)

==> either (x-8)=0 or (x+3) = 0

==> x-8=0 ==>x = 8

x + 3 = 0 ==> x = -3

so the possible numbers are 8 or -3

We can also apply quadratic formula to solve the equation

Regards.
praseenakos@yahoo.co.in

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