the ratio of ten more than three times a number to the square of the same number is equal to one. what is the number?

See my previous reply to your earlier post of this

sorry for not seeing and thank you. :-)

To solve this problem, let's break it down step by step.

Let's assume the number is represented by the variable "x".

The ratio of ten more than three times a number (3x + 10) to the square of the same number (x^2) is equal to one. Mathematically, this can be expressed as:

(3x + 10) / (x^2) = 1

To find the value of "x," we need to solve this equation.

First, let's multiply both sides of the equation by (x^2) to eliminate the denominator:

(x^2) * (3x + 10) / (x^2) = 1 * (x^2)

Simplifying, we get:

3x + 10 = x^2

Now, we have a quadratic equation. Let's move all the terms to one side:

x^2 - 3x - 10 = 0

To solve this quadratic equation, we can either factor it or use the quadratic formula. In this case, the quadratic equation doesn't factor easily, so let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 1, b = -3, and c = -10. Plugging these values into the quadratic formula:

x = (-(-3) ± √((-3)^2 - 4 * 1 * (-10))) / (2 * 1)

Simplifying further:

x = (3 ± √(9 + 40)) / 2

x = (3 ± √49) / 2

x = (3 ± 7) / 2

Now, we have two possible solutions:

1. If we take the positive value of the square root:

x = (3 + 7) / 2
x = 10 / 2
x = 5

2. If we take the negative value of the square root:

x = (3 - 7) / 2
x = -4 / 2
x = -2

Therefore, the possible solutions for the number are x = 5 or x = -2.