Question

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

variable. Then find the solution using guess-check-and-improve.
7 added to the square of a number is equal to 7 times the number,
minus 5. What is the number? (There are two solutions.)
a. 7 + x = 7x − 5, 2 c. 7 + x2 = 7x − 5, 2 or 3
b. 7 + x2 = 7x − 5, 3 or 4 d. 7 + x2 = 7x − 5, 4 or 5

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