3n^2-14n-45=0

Simple and best practice solution for 3n^2-14n-45=0 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 3n^2-14n-45=0 equation: 


Simplifying
3n2 + -14n + -45 = 0

Reorder the terms:
-45 + -14n + 3n2 = 0

Solving
-45 + -14n + 3n2 = 0

Solving for variable 'n'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-15 + -4.666666667n + n2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -4.666666667n + 15 + n2 = 0 + 15

Reorder the terms:
-15 + 15 + -4.666666667n + n2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4.666666667n + n2 = 0 + 15
-4.666666667n + n2 = 0 + 15

Combine like terms: 0 + 15 = 15
-4.666666667n + n2 = 15

The n term is -4.666666667n.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667n + 5.444444448 + n2 = 15 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667n + n2 = 15 + 5.444444448

Combine like terms: 15 + 5.444444448 = 20.444444448
5.444444448 + -4.666666667n + n2 = 20.444444448

Factor a perfect square on the left side:
(n + -2.333333334)(n + -2.333333334) = 20.444444448

Calculate the square root of the right side: 4.521553322

Break this problem into two subproblems by setting 
(n + -2.333333334) equal to 4.521553322 and -4.521553322.


Subproblem 1
n + -2.333333334 = 4.521553322

Simplifying
n + -2.333333334 = 4.521553322

Reorder the terms:
-2.333333334 + n = 4.521553322

Solving
-2.333333334 + n = 4.521553322

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + n = 4.521553322 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + n = 4.521553322 + 2.333333334
n = 4.521553322 + 2.333333334

Combine like terms: 4.521553322 + 2.333333334 = 6.854886656
n = 6.854886656

Simplifying
n = 6.854886656


Subproblem 2
n + -2.333333334 = -4.521553322

Simplifying
n + -2.333333334 = -4.521553322

Reorder the terms:
-2.333333334 + n = -4.521553322

Solving
-2.333333334 + n = -4.521553322

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + n = -4.521553322 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + n = -4.521553322 + 2.333333334
n = -4.521553322 + 2.333333334

Combine like terms: -4.521553322 + 2.333333334 = -2.188219988
n = -2.188219988

Simplifying
n = -2.188219988


Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {6.854886656, -2.188219988}

See similar equations:

| -76+45= | | -48+55= | | 81+(-90)= | | 6(x-4)=-4(x+1)+46 | | 2y^2=3y+7 | | -7(6+9m)-3= | | -50+-20= | | 3m^2-13m+8=0 | | -56+-4= | | 8(0.25+0.125y)-y=2 | | 4(x+2)=8(x-2)-4 | | 4(x-2)=-5(x+4)+45 | | -42-3= | | 6x^2-12x-8=10 | | 4x+5-2x=7+4x-6 | | -2z+1=6 | | 126*10x= | | 8+e^2x+3=11 | | -0.3(0.5+6.5b)= | | -27x-3=180 | | 4x^3-54x^2+180x+100=0 | | -27x-3=360 | | -3y-10=-4 | | 58x-136=-20 | | 20=11a^2-32a+17 | | 2c-(c-6)=4(c-2) | | 7x=5(x+12) | | 5/4x-7y/6 | | 3(2x-1)-(4-x)=14 | | 4.2+x=6.9 | | 4(3x+3)+18=8x-2 | | 4cos(4x+1)=0 |

Equations solver categories