Question

A number has the property that its square is equal to 84 more than five times the number. Enter all numbers that have this property.

Answer 1

Answer:

The numbers for which the given property hold true are 12 and -7

Step-by-step explanation:

Let the number be $x$.

As per the given statement:

Square of the number ($x^{2}$) is 84 more than five times of the number ($5x+84$).

Writing in the equation form:

$x^{2} =5x+84$

To find:

All the numbers for which above equation holds true.

Solution:

$x^{2} =5x+84$

Let us solve the above equation by rearranging the terms and then let us find the roots of the equation.

It is a quadratic equation(i.e. maximum power of $x$ is 2) so it will have 2 solutions  i.e. 2 values of $x$ for which the above equation will hold true.

$x^{2} -5x-84=0$

Let us factorize the equation.

$\Rightarrow x^{2} -12x+7x-84=0\\\Rightarrow x(x -12)+7(x-12)=0\\\Rightarrow (x+7)(x-12)=0\\\Rightarrow \bold{x=12, -7 }$

So, the numbers for which the given property hold true are 12 and -7.