Question

Four times the square of a number increased by five times the same number

Answer 1

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, 4x2 = 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" (4x2)

3. the word 'is' typically indicates "equal to" (4x2 =)

4. the 45 given (4x2 = 45)

5. the words, 'more than' typically mean to add to something so that is where the addition comes from (4x2 = 45 +)

6. "8 times the number" refers to 8 times the same number that was spoken of in the first part of the question (4x2 = 45 + 8x)

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

Answer 2

Here we have to configure an algebraic expression from the information.

Let us do it step by step as follow:

Step 1:

let us say the number is x.

square of the number will be x²

Step 2:

four times square of the number , here we multiply the expression found above with 4 to get 4*x²

Step 3:

five times the same number will be 5x

Step 4:

now we relate the expression of step 2 and 3 with the given information as

the expression found in step 2 is increased by the expression found in step 3, by increased here we mean adding the two expressions.

so our final expression would be:

4x² +5x