Question 922·Easy·Math

0 / 2000

Solve for the positive value of $n$ in the equation

n^2 + 2n = 48

A quadratic equation has a squared variable, so it may have two solutions. The word positive tells you which one to keep. Factoring can reveal how the terms fit together; then a Desmos regression with a positive restriction can find the requested value. Choose a solution with the required sign; don't change a solution's sign.

Hints

Hint 1
Both $n^2$ and $2n$ have a shared factor of $n$ . Use factoring to rewrite the left side as $n(n+2)$ . What must the product of those two factors equal?
Hint 2
The two factors are $n$ and $n+2$ , so they're two apart. A regression can solve their product equation in Desmos; how could you tell it to look only for a positive value of $n$ ?

Step-by-step

Factor, then solve in Desmos
Step 1
Show the relationship between the factors
Factoring means pulling out a shared multiplier. Both terms on the left contain $n$ , so rewrite the equation:
$n(n+2)=48.$
The factors must multiply to $48$ , but they must also be two apart. Not every factor pair of $48$ works.
Step 2
Find the positive solution
Type $n(n+2)\sim48\{n>0\}$ in Desmos. The $\sim$ tells Desmos to solve for $n$ , and the restriction in braces keeps only positive values. Desmos shows $n=6$ under PARAMETERS. So the positive value of $n$ is $6$ . Choice C.

Question 922·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this