3n2+9n=363

Move 363 to the left side of the equation by subtracting it from both sides.

3n2+9n-363=0

Factor 3 out of 3n2.

3(n2)+9n-363=0

Factor 3 out of 9n.

3(n2)+3(3n)-363=0

Factor 3 out of -363.

3n2+3(3n)+3⋅-121=0

Factor 3 out of 3n2+3(3n).

3(n2+3n)+3⋅-121=0

Factor 3 out of 3(n2+3n)+3⋅-121.

3(n2+3n-121)=0

3(n2+3n-121)=0

Divide each term in 3(n2+3n-121)=0 by 3.

3(n2+3n-121)3=03

Cancel the common factor of 3.

Cancel the common factor.

3(n2+3n-121)3=03

Divide n2+3n-121 by 1.

n2+3n-121=03

n2+3n-121=03

Divide 0 by 3.

n2+3n-121=0

n2+3n-121=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=1, b=3, and c=-121 into the quadratic formula and solve for n.

-3±32-4⋅(1⋅-121)2⋅1

Simplify the numerator.

Raise 3 to the power of 2.

n=-3±9-4⋅(1⋅-121)2⋅1

Multiply -121 by 1.

n=-3±9-4⋅-1212⋅1

Multiply -4 by -121.

n=-3±9+4842⋅1

Add 9 and 484.

n=-3±4932⋅1

n=-3±4932⋅1

Multiply 2 by 1.

n=-3±4932

n=-3±4932

The final answer is the combination of both solutions.

n=-3-4932,-3+4932

The result can be shown in multiple forms.

Exact Form:

n=-3-4932,-3+4932

Decimal Form:

n=9.60180165…,-12.60180165…

Solve for n 3n^2+9n=363