n^2=10n+5

Simple and best practice solution for n^2=10n+5 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=10n+5 equation:


Simplifying
n2 = 10n + 5

Reorder the terms:
n2 = 5 + 10n

Solving
n2 = 5 + 10n

Solving for variable 'n'.

Reorder the terms:
-5 + -10n + n2 = 5 + 10n + -5 + -10n

Reorder the terms:
-5 + -10n + n2 = 5 + -5 + 10n + -10n

Combine like terms: 5 + -5 = 0
-5 + -10n + n2 = 0 + 10n + -10n
-5 + -10n + n2 = 10n + -10n

Combine like terms: 10n + -10n = 0
-5 + -10n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -10n + 5 + n2 = 0 + 5

Reorder the terms:
-5 + 5 + -10n + n2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -10n + n2 = 0 + 5
-10n + n2 = 0 + 5

Combine like terms: 0 + 5 = 5
-10n + n2 = 5

The n term is -10n.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10n + 25 + n2 = 5 + 25

Reorder the terms:
25 + -10n + n2 = 5 + 25

Combine like terms: 5 + 25 = 30
25 + -10n + n2 = 30

Factor a perfect square on the left side:
(n + -5)(n + -5) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(n + -5) equal to 5.477225575 and -5.477225575.

Subproblem 1

n + -5 = 5.477225575 Simplifying n + -5 = 5.477225575 Reorder the terms: -5 + n = 5.477225575 Solving -5 + n = 5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = 5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + n = 5.477225575 + 5 n = 5.477225575 + 5 Combine like terms: 5.477225575 + 5 = 10.477225575 n = 10.477225575 Simplifying n = 10.477225575

Subproblem 2

n + -5 = -5.477225575 Simplifying n + -5 = -5.477225575 Reorder the terms: -5 + n = -5.477225575 Solving -5 + n = -5.477225575 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + n = -5.477225575 + 5 Combine like terms: -5 + 5 = 0 0 + n = -5.477225575 + 5 n = -5.477225575 + 5 Combine like terms: -5.477225575 + 5 = -0.477225575 n = -0.477225575 Simplifying n = -0.477225575

Solution

The solution to the problem is based on the solutions from the subproblems. n = {10.477225575, -0.477225575}

See similar equations:

| 1/6k= | | 5x-8=8x-26 | | -5c-4(-3)=13 | | -24+4x=-20 | | 2(x-8)+9x=6 | | (p-3)(3p+2)(p+2)=0 | | 0.4(x+.07)=.06(x-4.2) | | 4x+10=2(6x-3) | | 3/x=5/45 | | P=W/t(w) | | -5-6(1-a)=-5(7-6a) | | y=1/2(1)-1 | | x+2x+5+3x+2+6x-17= | | 6x-7=2x-15 | | (5x-10)-2=-13 | | 15x-28=3x+92 | | x^2+6x-35=180 | | 4x+(-x-17)=2 | | 3r^2-12r-3=6-2r^2 | | C=50m+50 | | 5x-10-2=-13 | | 15x-28=3x | | L/0.8=4.9 | | -5/2x=34 | | 12+14y=330 | | 14a-2b=4 | | 0.47x-20=0.9x+3.25 | | 11x(x+2)+7x+3= | | y-13=-8x^2+6x-12 | | x+7y=35 | | m^2-2m=-6m+5 | | 5/8(y-2/5)=-4/12 |

Equations solver categories