3 times a number is 4 less than the square of that number. Find the negative solution

Factorization, often known as factoring, is the process of expressing a number or another mathematical object or mathematical equations as a product of several factors.

Now, In the given question let's first assume that the unknown number is a variable x.

So, 3 times that number is (3 × x)

And then, 4 less than the square of that number is (x² - 4)

Now, as the question states that 3 times a number is 4 less than the square of that number,

So we can write,

3x = x² - 4

Now, we have to solve this quadratic equation with the help of factorization.

To solve the quadratic equation we first bring all the terms to any of the sides and after rearranging a little the equation is as follows:

x² - 3x - 4 = 0

Now, if we want to find the factors in the form ax² + bx + c we need to multiply a and c and then we have to identify what two numbers sum up to b and multiply to ac.

Here, a = 1, b = -3 and c = -4

Now, ac = -4

So, we have to identify what two numbers sum up to b and multiply to ac. The numbers are -4 and 1 and we can check that they sum up to -3 and multiply to -4.

So first we have to split the equation: x² - 3x - 4 = 0

x² - 4x + 1x - 4 = 0

Now, we have to group the above equation,

(x² - 4x) + (1x - 4) = 0

Taking x common from the first group and taking 1 common from the second group we get,

(x)(x - 4) + (1)(x - 4) = 0

Now, again taking (x - 4) common from the equation we get,

(x - 4) × (x + 1) = 0

So, we set each factor to zero now,

(x - 4) = 0

Adding 4 to each side of the equation we get,

x - 4 + 4 = 4

Simplifying we get,

x = 4

(x + 1) = 0

Adding -1 to each side of the equation we get,

x + 1 - 1 = -1

Simplifying we get,

x = -1

So, we now have two solutions of x that is 4 and -1

But according to the question we only need the negative one.

Therefore, the negative solution is -1

To know more about how to solve quadratic equations by factorization

use this - brainly.com/question/544930

#SPJ2