# the square of a number is 6 more than the number. find the number.?

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x²  =  x  +  6

x²  -  x  -  6  = 0

( x  - 3 ) ( x. + 2 ) = 0

x.  = 3 , x   = - 2

The number could be 3 or - 2

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• x^2 = x + 6

x^2 - x - 6 = 0

(x - 3)(x + 2) = 0

x = 3 or x = -2

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• x^2 = x + 6

(x - 3)(x + 2) = 0

x = -2

x = 3

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• The number is 3 because 3^2 = 3+6

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• x^2 - x - 6 = 0

(x - 3)(x + 2) = 0

x = -2

x = 3

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• A^2=A+6

A=3     3*3=9, 3+6=9

A=  -2  -2*-2=4,  -2+6=4

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• The number is N

the square of the number

N-squared

is 6 more than the number

N + 6 = N-squared

You can set it equal to zero

0 = N-squared - N - 6

and then use the binomial equation

or factor

Factoring

we get

0 = (N - 3)(N + 2)

So

N is EITHER

+3

or

-2

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• x^2 = x + 6

x^2 - x - 6 = 0

x = (1 +/- sqrt(1 + 24)) / 2

x = (1 +/- sqrt(25)) / 2

x = (1 +/- 5) / 2

x = -4/2 , 6/2

x = -2 , 3

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• The number is either 3 or -2.

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