5n^2=-3n+12

Simple and best practice solution for 5n^2=-3n+12 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 5n^2=-3n+12 equation:


Simplifying
5n2 = -3n + 12

Reorder the terms:
5n2 = 12 + -3n

Solving
5n2 = 12 + -3n

Solving for variable 'n'.

Reorder the terms:
-12 + 3n + 5n2 = 12 + -3n + -12 + 3n

Reorder the terms:
-12 + 3n + 5n2 = 12 + -12 + -3n + 3n

Combine like terms: 12 + -12 = 0
-12 + 3n + 5n2 = 0 + -3n + 3n
-12 + 3n + 5n2 = -3n + 3n

Combine like terms: -3n + 3n = 0
-12 + 3n + 5n2 = 0

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

Divide each side by '5'.
-2.4 + 0.6n + n2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 0.6n + 2.4 + n2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 0.6n + n2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 0.6n + n2 = 0 + 2.4
0.6n + n2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
0.6n + n2 = 2.4

The n term is 0.6n.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6n + 0.09 + n2 = 2.4 + 0.09

Reorder the terms:
0.09 + 0.6n + n2 = 2.4 + 0.09

Combine like terms: 2.4 + 0.09 = 2.49
0.09 + 0.6n + n2 = 2.49

Factor a perfect square on the left side:
(n + 0.3)(n + 0.3) = 2.49

Calculate the square root of the right side: 1.577973384

Break this problem into two subproblems by setting 
(n + 0.3) equal to 1.577973384 and -1.577973384.

Subproblem 1

n + 0.3 = 1.577973384 Simplifying n + 0.3 = 1.577973384 Reorder the terms: 0.3 + n = 1.577973384 Solving 0.3 + n = 1.577973384 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + n = 1.577973384 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + n = 1.577973384 + -0.3 n = 1.577973384 + -0.3 Combine like terms: 1.577973384 + -0.3 = 1.277973384 n = 1.277973384 Simplifying n = 1.277973384

Subproblem 2

n + 0.3 = -1.577973384 Simplifying n + 0.3 = -1.577973384 Reorder the terms: 0.3 + n = -1.577973384 Solving 0.3 + n = -1.577973384 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + n = -1.577973384 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + n = -1.577973384 + -0.3 n = -1.577973384 + -0.3 Combine like terms: -1.577973384 + -0.3 = -1.877973384 n = -1.877973384 Simplifying n = -1.877973384

Solution

The solution to the problem is based on the solutions from the subproblems. n = {1.277973384, -1.877973384}

See similar equations:

| 7/10-3=10 | | -6-4(n+1)=-n-25 | | -4p+23=-(p+1) | | 5x+6=10x-14 | | -3n-5+n-6=6(1-n)-7(3n+6) | | 9n^2+10=-8n | | -7x+18=3 | | 60/x^225 | | 8(p+4)=64 | | 5-n=-3(n-1) | | X+X+18=762 | | 13x-10.4=1x+8.8 | | 3x+14+2x-29+4x-25+(x+10)=360 | | -5(3-7x)=39+8x | | y=175-15x | | 3+p=i | | -log(10)=log(x) | | 13x=x+19.2 | | 2y+5+17y+8= | | -48=-4-z | | 5b+7-5=14+7b+2b | | 0.01k=100 | | -5v+16=1-2v | | n+2=-11-4n-8n | | P=x^4+5x^2-32 | | 7-4x=-5x+5 | | 2*3.14*x=11 | | ln4/ln3 | | 890=50+35(x+75) | | -16-7v-1+v=v+4 | | -6(-3+2x)=102 | | m/3-2=2 |

Equations solver categories