Question

Write an equation to represent the number puzzle. Use x as the

Answer 1

The equation is:

$x^2 - 7x + 12 = 0$

The number is 3 or 4

Solution:

Given that,

7 added to the square of a number is equal to 7 times the number,  minus 5

Let "x" be the unknown number

From given,

7 added to square of x = 7 times the x minus, 5

$7 + x^2 = 7x - 5$

Solve the above equation

$x^2 -7x +7+5 = 0\\\\x^2 - 7x + 12 = 0$

Split the middle term

$x^2 -3x - 4x + 12 = 0\\\\Group\ the\ expressions\\\\(x^2-3x) -(4x - 12) = 0\\\\Take\ the\ common\ factor\ out\\\\x(x -3) -4(x -3) = 0\\\\(x-3)(x-4) = 0$

We have two solutions

x - 3 = 0

x = 3

And

x - 4 = 0

x = 4

Thus number is 3 or 4