2n^2+2n-685=0

Simple and best practice solution for 2n^2+2n-685=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 2n^2+2n-685=0 equation:


Simplifying
2n2 + 2n + -685 = 0

Reorder the terms:
-685 + 2n + 2n2 = 0

Solving
-685 + 2n + 2n2 = 0

Solving for variable 'n'.

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

Divide each side by '2'.
-342.5 + n + n2 = 0

Move the constant term to the right:

Add '342.5' to each side of the equation.
-342.5 + n + 342.5 + n2 = 0 + 342.5

Reorder the terms:
-342.5 + 342.5 + n + n2 = 0 + 342.5

Combine like terms: -342.5 + 342.5 = 0.0
0.0 + n + n2 = 0 + 342.5
n + n2 = 0 + 342.5

Combine like terms: 0 + 342.5 = 342.5
n + n2 = 342.5

The n term is n.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + n2 = 342.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + n2 = 342.5 + 0.25

Combine like terms: 342.5 + 0.25 = 342.75
1.25 + n2 = 342.75

Factor a perfect square on the left side:
(n + 0.5)(n + 0.5) = 342.75

Calculate the square root of the right side: 18.513508582

Break this problem into two subproblems by setting 
(n + 0.5) equal to 18.513508582 and -18.513508582.

Subproblem 1

n + 0.5 = 18.513508582 Simplifying n + 0.5 = 18.513508582 Reorder the terms: 0.5 + n = 18.513508582 Solving 0.5 + n = 18.513508582 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = 18.513508582 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = 18.513508582 + -0.5 n = 18.513508582 + -0.5 Combine like terms: 18.513508582 + -0.5 = 18.013508582 n = 18.013508582 Simplifying n = 18.013508582

Subproblem 2

n + 0.5 = -18.513508582 Simplifying n + 0.5 = -18.513508582 Reorder the terms: 0.5 + n = -18.513508582 Solving 0.5 + n = -18.513508582 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + n = -18.513508582 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + n = -18.513508582 + -0.5 n = -18.513508582 + -0.5 Combine like terms: -18.513508582 + -0.5 = -19.013508582 n = -19.013508582 Simplifying n = -19.013508582

Solution

The solution to the problem is based on the solutions from the subproblems. n = {18.013508582, -19.013508582}

See similar equations:

| -[9x-(2x+3)]=-6-[4(3x-4)-3x] | | 7x-6x=72+x | | 10+8z=z-5 | | X^15=23838 | | 9+9n=7n+9 | | 10x+20(43-x)=590 | | 10x+20(x-43)=590 | | x^2-(3k-2)x+(k^2-1)=0 | | x=14*3*4 | | 1.3x+5=-35 | | x=15*3*4 | | =15*3*4 | | 4x-(3y-3x)-8y= | | x+10x+25(35-2x)=407 | | -3x=1/ | | 15x+2y-3+5y-6= | | 4x-1=7+x | | 2xy+3x=0 | | 6x(2x+3)=390 | | 18.84=12*3.14 | | 2x-11=5x+1 | | 0y=-4 | | X+15=x*4 | | 7x-(2x+3)=9(x-1) | | Xa+15=x*4 | | 3x+1=4x+8 | | x+8x=3+x | | Y+y+15=23 | | 15/10x4= | | y=-1X+20 | | f(1)=5x^2+100 | | -.2(1-x)=4(4+.1x) |

Equations solver categories