How to do this mathematics?!?

Question

The sum of a positive number and its square is 56.Find the number.

Answer 1

X will be our positive number, so

X + X^2 = 56
X^2 + X - 56 = 0
This is a cuadratic ecuation
U must solve it using the next expresion

X[1,2] = [ (b +- (b^2 - 4ac) ^1/2 ] / 2a

A is the coeficient next to X^2, b next to X and c is "alone"

Example a X^2 + b X + c = 0

In your case a = 1, b = 1 and c = -56
The ecuation may have 2 solutions, pay attention to that. But you shoud use the one positive, in this case is X = 7
Hope it helps...

Answer 2

7

Answer 3

7

Answer 4

let the number be x
let its square be x^2
x+x^2=56
x^2+x-56=0
x^2+8x-7x-56=0
x(x+8)-7(x+8)=0
(x-7)(x+8)=0
x-7=0 x+8=0
x=7 x=-8
since x is positive x=7

Answer 5

Let a is a positive number. You should solve the equation:
a^2+a-56=0
The only positive solution is a=7.

Answer 6

X^2+X=56
X(X+1)=56 & as you see X(X+1) are the mutiplication of two successive natural numbers. So, X(X+1)=7*8 Then we get:
X=7 & X+1=8 ==> X=7 again.

Answer 7

x + x*x = 56
7 + 7*7 = 7 +49 = 56

Answer 8

Let it be x
we have x^2+x = 56
or x^2+x - 56 =0
(x-7)(x+8) = 0
x = 7 or -8
but x is positve so 7

Answer 9

Let the no. be x.
So x+x2=56
or x2+x-56=0
or x2+8x-7x-56=0
or x(x+8)-7(x+8)=0
or (x+8)(x-7)=0
So either x=-8 or x=7
But since x is positive, so x=7.
[ x2 denotes x-squared]

Answer 10

You don't need algebra to solve this :)
You can solve this mentally....
The sum of number and its square is same as multiplying a number by its consecutive number.
Now 56 can be converted into 1x56, 2x28, 4x14, 7x8 so the obvious answer is from 7x8
i.e. the number is 7