When 8 is subtracted from the square of a number, the result is 7 times the number. Find the positive solution

Given the statement:

8 is subtracted from the square of a number, the result is 7 times the number.

It can be represented in numerical expression as,

8 - x^2 =7x

or 

x^2 + 7x -8

Find the positive solution.

Solution:

In order to solve for the roots of the quadratic equation, we simply must look at the 2nd and 3rd values. First, we must think of two numbers that when added, the answer is 7, and when multiplied, the answer is -8. Hence, if we are unable to find the number, we will use the quadratic formula. In our case, 8 and -1 can suffice the given condition

= (x + 8) (x - 1)

We can check this by using the FOIL method. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.

To clearly see how it works, here's a step by step solution.
 

= (x)(x)
=x^2
First term of the first equation multiplied to the first term of the second equation.

=(x)(-1)
= x
First term of the first equation multiplied to the last term of the second equation.

=(8)(x)
=8x
Last term of the first equation multiplied to the first term of the second equation.

=(8)(-1)
= -8
Last term of the first equation multiplied to the fast term of the second equation.

= x^2 - x + 8x - 8

= x^2 + 7x - 8

Since we've confirmed that the factors are true, now we need to equate each factor to 0 and solve for x.

( x + 8)

x + 8 =0

x = -8

(x - 1)

x - 1 = 0

x = 1

Final answer:

x = -8

x = 1