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7 times a number is 8 less than the square of that number. Find the positive solution.

8

Step-by-step explanation:

Let's just call the number x for simplicity.

So, 7x is 8 less than x².

Putting this into an equation would look like this

x² - 8 = 7x

It looks like we'll have to factor this to solve. Before we do that we need to move the 7x to the left side so that everything is together.

x² - 7x -8 = 0

Now, we can proceed. To factor we first need to find the factors of -8.

The factors of -8 are

-2 ⋅ 4, -4 ⋅ 2, -1 ⋅ 8, 1 ⋅ -8.

We need to find the pair of factors that adds up to -7. The only ones that do are -1 and 8.

So now that we have these we can create a pair of binomials using them. This will give us the factored form of this equation.

( x + 1 ) ( x - 8 )

To find the solutions we will have to set them to 0 and solve each of these binomials individually.

x - 1 = 0

x = 1

So, one of the solutions is 1. It's not the one we want, since it's positive.

x - 8 = 0

x = 8

This is the one we want since it is positive.

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step-by-step explanation: