n^2+2n-3=7

Simple and best practice solution for n^2+2n-3=7 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-3=7 equation:


Simplifying
n2 + 2n + -3 = 7

Reorder the terms:
-3 + 2n + n2 = 7

Solving
-3 + 2n + n2 = 7

Solving for variable 'n'.

Reorder the terms:
-3 + -7 + 2n + n2 = 7 + -7

Combine like terms: -3 + -7 = -10
-10 + 2n + n2 = 7 + -7

Combine like terms: 7 + -7 = 0
-10 + 2n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + 2n + 10 + n2 = 0 + 10

Reorder the terms:
-10 + 10 + 2n + n2 = 0 + 10

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

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

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 = 10 + 1

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

Combine like terms: 10 + 1 = 11
1 + 2n + n2 = 11

Factor a perfect square on the left side:
(n + 1)(n + 1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(n + 1) equal to 3.31662479 and -3.31662479.

Subproblem 1

n + 1 = 3.31662479 Simplifying n + 1 = 3.31662479 Reorder the terms: 1 + n = 3.31662479 Solving 1 + n = 3.31662479 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 = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + n = 3.31662479 + -1 n = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 n = 2.31662479 Simplifying n = 2.31662479

Subproblem 2

n + 1 = -3.31662479 Simplifying n + 1 = -3.31662479 Reorder the terms: 1 + n = -3.31662479 Solving 1 + n = -3.31662479 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 = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + n = -3.31662479 + -1 n = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 n = -4.31662479 Simplifying n = -4.31662479

Solution

The solution to the problem is based on the solutions from the subproblems. n = {2.31662479, -4.31662479}

See similar equations:

| -3b-b(7b-8)= | | 3(2x+3)=20 | | 2(4x+1)-3(X-2)=2(2x-5) | | 2r-t=0 | | 4x-17=0 | | x-23=-23 | | H+12=68 | | lg(1-2y)=8 | | 12-(7+3x)= | | 31(x-2)= | | 8y(-1x)= | | X+3-4x=15 | | 300mm=0.m | | 300mm= | | 14m-9m=-120 | | 8y(-1y)= | | 180-(7x+-28)=5x+64 | | 8x-3=4(2x-4) | | 4x-1-2=2 | | 4n+=17 | | 24x+60=9x | | -9x-3x=-7 | | -3(6+3x)=-7 | | .5e=.75 | | 180-(5x+55)=9x+27 | | 4(1.20+b)=7.20 | | X+8.2=12.4 | | 5x^2-41x=-66 | | y=-2+2x+1.75 | | 180-(5x+55)=9x | | -2y=4-4x | | 5x+8-7x=4x+1 |

Equations solver categories