2n^2=-10n-1

Simple and best practice solution for 2n^2=-10n-1 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=-10n-1 equation:


Simplifying
2n2 = -10n + -1

Reorder the terms:
2n2 = -1 + -10n

Solving
2n2 = -1 + -10n

Solving for variable 'n'.

Reorder the terms:
1 + 10n + 2n2 = -1 + -10n + 1 + 10n

Reorder the terms:
1 + 10n + 2n2 = -1 + 1 + -10n + 10n

Combine like terms: -1 + 1 = 0
1 + 10n + 2n2 = 0 + -10n + 10n
1 + 10n + 2n2 = -10n + 10n

Combine like terms: -10n + 10n = 0
1 + 10n + 2n2 = 0

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

Divide each side by '2'.
0.5 + 5n + n2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 5n + -0.5 + n2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 5n + n2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 5n + n2 = 0 + -0.5
5n + n2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
5n + n2 = -0.5

The n term is 5n.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5n + 6.25 + n2 = -0.5 + 6.25

Reorder the terms:
6.25 + 5n + n2 = -0.5 + 6.25

Combine like terms: -0.5 + 6.25 = 5.75
6.25 + 5n + n2 = 5.75

Factor a perfect square on the left side:
(n + 2.5)(n + 2.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(n + 2.5) equal to 2.397915762 and -2.397915762.

Subproblem 1

n + 2.5 = 2.397915762 Simplifying n + 2.5 = 2.397915762 Reorder the terms: 2.5 + n = 2.397915762 Solving 2.5 + n = 2.397915762 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = 2.397915762 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = 2.397915762 + -2.5 n = 2.397915762 + -2.5 Combine like terms: 2.397915762 + -2.5 = -0.102084238 n = -0.102084238 Simplifying n = -0.102084238

Subproblem 2

n + 2.5 = -2.397915762 Simplifying n + 2.5 = -2.397915762 Reorder the terms: 2.5 + n = -2.397915762 Solving 2.5 + n = -2.397915762 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + n = -2.397915762 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + n = -2.397915762 + -2.5 n = -2.397915762 + -2.5 Combine like terms: -2.397915762 + -2.5 = -4.897915762 n = -4.897915762 Simplifying n = -4.897915762

Solution

The solution to the problem is based on the solutions from the subproblems. n = {-0.102084238, -4.897915762}

See similar equations:

| 3y+5=4(9+0,75y) | | -38-10x=-32-8x | | 4x^2-25x+8=0 | | 23=9/5c+32 | | a/3=-2 | | 2/3x4 | | 2x+16-6=0 | | a/(x-1)+a/(x+1) | | (16x^3-9x-16x^2+9)/(x-1) | | 9x-4x+(4+x)=2(x-1) | | -39+x=-41 | | 10r^2-9r+2=0 | | (6y-18)=(2y+6) | | ln(7x+6)=4 | | 4a^2+4a+1/2a^2+3a+1 | | 10x-14=26 | | 2/3*21 | | 5+x=(24-x)-(19-2x) | | x-6+x=28 | | Y+.75x=4 | | 6-6(3x-2)=0 | | (-3x^6y^3)/9x^2y^2 | | -1/3p-7=-3 | | 5/3+2/3x=48/18+7/6x+5/6 | | 5c^2-14c-3=0 | | 3y=7y+7 | | x^2-10+29=0 | | 2*2/3 | | 6+5x-2=8x+19-6x | | Y^2-16y+39=0 | | 6+0=-2+2v | | 5x^2-3x-12=0 |

Equations solver categories