n^2+6n-3=0

Simple and best practice solution for n^2+6n-3=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 n^2+6n-3=0 equation:


Simplifying
n2 + 6n + -3 = 0

Reorder the terms:
-3 + 6n + n2 = 0

Solving
-3 + 6n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6n + 3 + n2 = 0 + 3

Reorder the terms:
-3 + 3 + 6n + n2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6n + n2 = 0 + 3
6n + n2 = 0 + 3

Combine like terms: 0 + 3 = 3
6n + n2 = 3

The n term is 6n.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6n + 9 + n2 = 3 + 9

Reorder the terms:
9 + 6n + n2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6n + n2 = 12

Factor a perfect square on the left side:
(n + 3)(n + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(n + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1

n + 3 = 3.464101615 Simplifying n + 3 = 3.464101615 Reorder the terms: 3 + n = 3.464101615 Solving 3 + n = 3.464101615 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + n = 3.464101615 + -3 n = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 n = 0.464101615 Simplifying n = 0.464101615

Subproblem 2

n + 3 = -3.464101615 Simplifying n + 3 = -3.464101615 Reorder the terms: 3 + n = -3.464101615 Solving 3 + n = -3.464101615 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + n = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + n = -3.464101615 + -3 n = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 n = -6.464101615 Simplifying n = -6.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. n = {0.464101615, -6.464101615}

See similar equations:

| 0.3x(2+4)+7= | | 0.3x-0.4y=2 | | 2=10+2.5x | | x-7-7=13 | | X+(x+8)+(x+16)+(x+24)+(x+32)=150 | | 4-8(z-3)= | | 3x-4=2/5 | | N/50=0.18N= | | y=10-2.5(3.2) | | 30=-5/9y | | 1.500000+3.2+0.2+0.2+0.2+0.50+1.50= | | sin(4x)-sin(x)=0 | | 5=9(6)+b | | 4+5a(3a-10)= | | w=525+-75(2) | | -8=x/7-5 | | 5(xy+8)=150 | | -6/7w=30 | | w=525+-75(1) | | 6=x/8-2 | | w=525+-7591 | | 17p+8-13-7p= | | -(4/3)2 | | 9t-1/2t-8 | | 2x-9=-8x+21 | | 6x+10=3x+2 | | 2x-6/3=10 | | 6x-14=3x | | 2x^2+176x-408=0 | | 6x+4(2x-3)=100 | | wy-8w+4y-2w^2=0 | | -5(6x-3)=375 |

Equations solver categories