n^2=2n+1

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


Simplifying
n2 = 2n + 1

Reorder the terms:
n2 = 1 + 2n

Solving
n2 = 1 + 2n

Solving for variable 'n'.

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

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -2n + 1 + n2 = 0 + 1

Reorder the terms:
-1 + 1 + -2n + n2 = 0 + 1

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

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

The n term is -2n.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2n + 1 + n2 = 1 + 1

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

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

Factor a perfect square on the left side:
(n + -1)(n + -1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(n + -1) equal to 1.414213562 and -1.414213562.

Subproblem 1

n + -1 = 1.414213562 Simplifying n + -1 = 1.414213562 Reorder the terms: -1 + n = 1.414213562 Solving -1 + n = 1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = 1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + n = 1.414213562 + 1 n = 1.414213562 + 1 Combine like terms: 1.414213562 + 1 = 2.414213562 n = 2.414213562 Simplifying n = 2.414213562

Subproblem 2

n + -1 = -1.414213562 Simplifying n + -1 = -1.414213562 Reorder the terms: -1 + n = -1.414213562 Solving -1 + n = -1.414213562 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + n = -1.414213562 + 1 Combine like terms: -1 + 1 = 0 0 + n = -1.414213562 + 1 n = -1.414213562 + 1 Combine like terms: -1.414213562 + 1 = -0.414213562 n = -0.414213562 Simplifying n = -0.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.414213562, -0.414213562}

See similar equations:

| x+xy+2(y^2)=6 | | 3x+4y+2z=8 | | 64-125a^3=0 | | 3b-2(b+3)=4b+6 | | 50+2y=y | | -2-(-12-13)-4+6= | | y+10+2y-40+2y-31+2y-40=180 | | -(-11-12)-(5-11)= | | b^3-g^3=0 | | 5y-61+x=180 | | 300-x=300-2y | | 5a-4=3a-6 | | 12d-8=0 | | y=2x^2+6x-2 | | 6x-(3x-14)=35+(15-6x) | | 3x-2=3-2x | | -(3x-2)=2x | | a^2-14az+48z^2=0 | | y^2-22y+120=0 | | 21+22m+m^2=0 | | 6x^3-11x^2-57x+20=0 | | 4w-12+w^2=0 | | 3q^2+11=5q | | 3x+28=11x-29 | | c^2-6c+5=0 | | 6.78+5.2x=-36.5 | | 2x+3y+13=0 | | t^2-6t=20+2t | | t^2-6-2t-20=0 | | 32-2x=7x+19 | | t^2-6+2t-20=0 | | ln(6x+3)=3 |

Equations solver categories