When 45 is subtracted from the square of a number, the result is 4 times the number. Find the positive solution.

Answer 1

To answer this question, I would put this into the form of an equation. It starts by stating 45 subtracted from the square of a number, so x² - 45. It then goes on to say that this is equal to 4 times the number, which would be 4x. This then gives us the equation x² - 45=4x. To solve this, we'll put it into the form x² - 4x - 45=0 which will make it easier to factor. This will factor into (x-9)(x+5)=0. Thus, x=9 or x=-5. Since it asks for the positive solution, the answer is x=9.

Answer 2

Let's first translate this problem into an equation.

Let's call unknown number x. When we subtract 45 from the square of x, we get 4 times x. This would correspond to x² - 45 = 4x. This is a quadratic equation, so we first move all the terms to one side of the equation. By subtracting 4x on both sides we get

x² - 4x - 45 = 0

Now, we attempt to factor x² - 4x - 45. The shortcut is to find two numbers a and b such that their product is -45 and their sum is -4. After some trial and error, you'll find that those numbers are -9 and +5 since -9×5=-45 and -9+5=-4. Now, we have (x-9)(x+5)=0.

We now set each factor equal to zero separately to find the solutions:

x-9=0

+9 +9

x=9

and

x+5=0

-5 -5

x=-5

Since we are only interested in the positive solution, the answer to the problem is 9

Answer 3

We can create an equation from this problem. "When 45 is subtracted from the square of a number, the result is 4 times the number" can be represented as the following equation:

x² - 45 = 4x

x² - 4x - 45 = 0 [Bring 4x to the left side to put it in the form of ax² + bx + c = 0]

Using the Quadratic Formula, we can solve for x:

Quadratic Formula: ( − b ± √ ( b² - 4ac ) ) / 2a

x = ( 4 ± √ ( 4² - 4 × 1 × -45 ) ) / (2 × 1)

x = ( 4 ± √196 ) / 2

x = (4 ± 14) / 2

x = 18 / 2 OR -10 / 2

x = 9 OR -5

The positive solution is x = 9.