Four times the square of a number is 45 more than eight times the number. What is the number?

The answer is tricky but it is -5/2 & 9/2.

This is an algebraic formula in the form of words. It looks like this, 4x^{2
}= 45 + 8x. I will breakdown how I got to the formula below.

1. four times a number means 4 times x because we do not know what "the number" is (4x)

2. the unknown number or 'x' is squared because the question says, "the square of a number" (4x^{2})

3. the word 'is' typically indicates "equal to" (4x^{2} =)

4. the 45 given (4x^{2} = 45)

5. the words, 'more than' typically mean to add to something so that is where the addition comes from (4x^{2} = 45 +)

6. "8 times the number" refers to 8 times the same number that was spoken of in the first part of the question (4x^{2} = 45 + 8x)

7. Now that we have the equation, we can solve for x.