I have no idea how this solved. Can anyone help?

label Algebra
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Three times the square of a certain positive number exceeds six times the number by nine.  Find the number:

Apr 27th, 2015

Read the words of the problem and convert it into an equation:

"Three times the square of a certain positive number"      3x^2

"Exceeds six times the number by nine"      6x + 9

These two expressions have to be equal:   3x^2 = 6x + 9

To solve we must set the quadratic equal to zero:  3x^2 - 6x - 9 = 0

We can factor out a 3:   3(x^2 - 2x - 3) = 0

Divide by 3:     x^2 - 2x - 3 = 0

Factor to solve:       (x - 3) (x + 1) = 0          x = 3  or x = -1

Since the original problem said the number was positive, "3" is the correct answer.

Apr 27th, 2015

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