N^2+35N-342=0

Simple and best practice solution for N^2+35N-342=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+35N-342=0 equation: 


Simplifying
N2 + 35N + -342 = 0

Reorder the terms:
-342 + 35N + N2 = 0

Solving
-342 + 35N + N2 = 0

Solving for variable 'N'.

Begin completing the square.

Move the constant term to the right:

Add '342' to each side of the equation.
-342 + 35N + 342 + N2 = 0 + 342

Reorder the terms:
-342 + 342 + 35N + N2 = 0 + 342

Combine like terms: -342 + 342 = 0
0 + 35N + N2 = 0 + 342
35N + N2 = 0 + 342

Combine like terms: 0 + 342 = 342
35N + N2 = 342

The N term is 35N.  Take half its coefficient (17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
35N + 306.25 + N2 = 342 + 306.25

Reorder the terms:
306.25 + 35N + N2 = 342 + 306.25

Combine like terms: 342 + 306.25 = 648.25
306.25 + 35N + N2 = 648.25

Factor a perfect square on the left side:
(N + 17.5)(N + 17.5) = 648.25

Calculate the square root of the right side: 25.460754113

Break this problem into two subproblems by setting 
(N + 17.5) equal to 25.460754113 and -25.460754113.


Subproblem 1
N + 17.5 = 25.460754113

Simplifying
N + 17.5 = 25.460754113

Reorder the terms:
17.5 + N = 25.460754113

Solving
17.5 + N = 25.460754113

Solving for variable 'N'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + N = 25.460754113 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + N = 25.460754113 + -17.5
N = 25.460754113 + -17.5

Combine like terms: 25.460754113 + -17.5 = 7.960754113
N = 7.960754113

Simplifying
N = 7.960754113


Subproblem 2
N + 17.5 = -25.460754113

Simplifying
N + 17.5 = -25.460754113

Reorder the terms:
17.5 + N = -25.460754113

Solving
17.5 + N = -25.460754113

Solving for variable 'N'.

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

Add '-17.5' to each side of the equation.
17.5 + -17.5 + N = -25.460754113 + -17.5

Combine like terms: 17.5 + -17.5 = 0.0
0.0 + N = -25.460754113 + -17.5
N = -25.460754113 + -17.5

Combine like terms: -25.460754113 + -17.5 = -42.960754113
N = -42.960754113

Simplifying
N = -42.960754113


Solution
The solution to the problem is based on the solutions
from the subproblems.
N = {7.960754113, -42.960754113}

See similar equations:

| 2x-18=y | | 10-10p=0 | | 4x+1-5x=6 | | 7(3)+y=16 | | 4w+-33=87 | | Xlnx-2x=0 | | 2y^2+4y+x-8=0 | | (4x+6)(2x-1)= | | 2(4x+1)+1=56 | | h(t)=-16t^2+vt | | -0.009x^2+4.05x+2=0 | | P=4x+qs-5 | | .05x+0.09975x+x=210 | | 35a-25-10a=0 | | 3w+5x-11y+3w+8x+2y= | | 8+6t+-3t+t= | | 2x+18-7=11 | | .3(x-100,000)=1,000,000 | | 3x+4(8)=12 | | 10x-17=2x+8 | | 4+7x=13-6x | | -6x=63+x | | PX=3+2QX | | 6-3t+2t=2-t+7 | | -3+7(x-2)=7(x+8) | | w^2-4w-117=0 | | 24-22=-4[1-6a] | | .13(50+x)=30 | | 2x-5y(1)=1 | | 2(8)+3y=6 | | 2x=80-y | | x-2sin(5x)=2 |

Equations solver categories