n^2+13n=240

Simple and best practice solution for n^2+13n=240 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for n^2+13n=240 equation:


Simplifying
n2 + 13n = 240

Reorder the terms:
13n + n2 = 240

Solving
13n + n2 = 240

Solving for variable 'n'.

Reorder the terms:
-240 + 13n + n2 = 240 + -240

Combine like terms: 240 + -240 = 0
-240 + 13n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + 13n + 240 + n2 = 0 + 240

Reorder the terms:
-240 + 240 + 13n + n2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + 13n + n2 = 0 + 240
13n + n2 = 0 + 240

Combine like terms: 0 + 240 = 240
13n + n2 = 240

The n term is 13n.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13n + 42.25 + n2 = 240 + 42.25

Reorder the terms:
42.25 + 13n + n2 = 240 + 42.25

Combine like terms: 240 + 42.25 = 282.25
42.25 + 13n + n2 = 282.25

Factor a perfect square on the left side:
(n + 6.5)(n + 6.5) = 282.25

Calculate the square root of the right side: 16.800297616

Break this problem into two subproblems by setting 
(n + 6.5) equal to 16.800297616 and -16.800297616.

Subproblem 1

n + 6.5 = 16.800297616 Simplifying n + 6.5 = 16.800297616 Reorder the terms: 6.5 + n = 16.800297616 Solving 6.5 + n = 16.800297616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = 16.800297616 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = 16.800297616 + -6.5 n = 16.800297616 + -6.5 Combine like terms: 16.800297616 + -6.5 = 10.300297616 n = 10.300297616 Simplifying n = 10.300297616

Subproblem 2

n + 6.5 = -16.800297616 Simplifying n + 6.5 = -16.800297616 Reorder the terms: 6.5 + n = -16.800297616 Solving 6.5 + n = -16.800297616 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + n = -16.800297616 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + n = -16.800297616 + -6.5 n = -16.800297616 + -6.5 Combine like terms: -16.800297616 + -6.5 = -23.300297616 n = -23.300297616 Simplifying n = -23.300297616

Solution

The solution to the problem is based on the solutions from the subproblems. n = {10.300297616, -23.300297616}

See similar equations:

| (61-2x)=(72-3x) | | 2(-2x+3)=46 | | h(t)=175(1.028) | | 3y=11x+13 | | 7.87-9.65x=8.52x-3.213 | | Wsquared-121=0 | | -4(y+6)+y-7= | | 4y+21=-2y-3 | | 2(x+150)=275 | | 4(3x+2)=7+12X | | 1.2c-6=1c+7 | | 6x^2-4x+32=0 | | 33(c+4)-7=-10 | | 9-5x=x-3 | | 10+5g=50 | | 9(-8)-8y=8 | | -3(x+5)+2(6x)=-20 | | x(2x+1)= | | 7w-(3w-7)=-9 | | x(.5)=6 | | (4m+9)-3(2m-5)=4m+9-6m-15 | | -38=4x-9 | | Xsquared+12x-30=12x+6 | | 72=2(l+w) | | 175=7x-4(7x+14) | | 9=2x+4+3x | | 7(7t+1)-16=t-(t+8) | | 5*x=36 | | 19=3z+1 | | 5sec^2x-20=0 | | 9(-10-9a)=3-12(3a-11) | | -74x-54=x-(-68) |

Equations solver categories