n^2=2(7n-23)

Simple and best practice solution for n^2=2(7n-23) 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=2(7n-23) equation:


Simplifying
n2 = 2(7n + -23)

Reorder the terms:
n2 = 2(-23 + 7n)
n2 = (-23 * 2 + 7n * 2)
n2 = (-46 + 14n)

Solving
n2 = -46 + 14n

Solving for variable 'n'.

Reorder the terms:
46 + -14n + n2 = -46 + 14n + 46 + -14n

Reorder the terms:
46 + -14n + n2 = -46 + 46 + 14n + -14n

Combine like terms: -46 + 46 = 0
46 + -14n + n2 = 0 + 14n + -14n
46 + -14n + n2 = 14n + -14n

Combine like terms: 14n + -14n = 0
46 + -14n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + -14n + -46 + n2 = 0 + -46

Reorder the terms:
46 + -46 + -14n + n2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + -14n + n2 = 0 + -46
-14n + n2 = 0 + -46

Combine like terms: 0 + -46 = -46
-14n + n2 = -46

The n term is -14n.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14n + 49 + n2 = -46 + 49

Reorder the terms:
49 + -14n + n2 = -46 + 49

Combine like terms: -46 + 49 = 3
49 + -14n + n2 = 3

Factor a perfect square on the left side:
(n + -7)(n + -7) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(n + -7) equal to 1.732050808 and -1.732050808.

Subproblem 1

n + -7 = 1.732050808 Simplifying n + -7 = 1.732050808 Reorder the terms: -7 + n = 1.732050808 Solving -7 + n = 1.732050808 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = 1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + n = 1.732050808 + 7 n = 1.732050808 + 7 Combine like terms: 1.732050808 + 7 = 8.732050808 n = 8.732050808 Simplifying n = 8.732050808

Subproblem 2

n + -7 = -1.732050808 Simplifying n + -7 = -1.732050808 Reorder the terms: -7 + n = -1.732050808 Solving -7 + n = -1.732050808 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + n = -1.732050808 + 7 Combine like terms: -7 + 7 = 0 0 + n = -1.732050808 + 7 n = -1.732050808 + 7 Combine like terms: -1.732050808 + 7 = 5.267949192 n = 5.267949192 Simplifying n = 5.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. n = {8.732050808, 5.267949192}

See similar equations:

| (4x^3)-(3x^2)=13 | | 6d-3d-2d+3-4d=0 | | y=2E-10x+0.3003 | | 9x-6x-5x= | | (4x^3)-(3x^2)=52 | | m^2-12m-16=-3 | | Y=6sinx+8cosx | | 16t+13=-35 | | -(4x-11)+2(3x+7)= | | X-126=12x+50 | | ×/2-5=-3 | | 4W-3=-15 | | 335=-5(-6x-13) | | 25=-9+3(a+5) | | 12+5t=3t-4 | | 3x-8=2+3x | | 9b+4a+2b-6a= | | 0=-2.3t^2+30t+6 | | 38/(6-5x)^2 | | (6-12i)/(-11) | | K/2-5#13 | | -4.5/0.75 | | 15+2x=4y | | -4(a-3)= | | 2x-94=122 | | S42/5 | | -11+1x=-7x-8(-x+1) | | x+y+z=2694 | | -161-12x=-x+92 | | V+b=-14 | | 6+21n=-50 | | 0=-1.75t^2+30t+6 |

Equations solver categories