n^2+10n-32=9

Simple and best practice solution for n^2+10n-32=9 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-32=9 equation:


Simplifying
n2 + 10n + -32 = 9

Reorder the terms:
-32 + 10n + n2 = 9

Solving
-32 + 10n + n2 = 9

Solving for variable 'n'.

Reorder the terms:
-32 + -9 + 10n + n2 = 9 + -9

Combine like terms: -32 + -9 = -41
-41 + 10n + n2 = 9 + -9

Combine like terms: 9 + -9 = 0
-41 + 10n + n2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 10n + 41 + n2 = 0 + 41

Reorder the terms:
-41 + 41 + 10n + n2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 10n + n2 = 0 + 41
10n + n2 = 0 + 41

Combine like terms: 0 + 41 = 41
10n + n2 = 41

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 = 41 + 25

Reorder the terms:
25 + 10n + n2 = 41 + 25

Combine like terms: 41 + 25 = 66
25 + 10n + n2 = 66

Factor a perfect square on the left side:
(n + 5)(n + 5) = 66

Calculate the square root of the right side: 8.124038405

Break this problem into two subproblems by setting 
(n + 5) equal to 8.124038405 and -8.124038405.

Subproblem 1

n + 5 = 8.124038405 Simplifying n + 5 = 8.124038405 Reorder the terms: 5 + n = 8.124038405 Solving 5 + n = 8.124038405 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 = 8.124038405 + -5 Combine like terms: 5 + -5 = 0 0 + n = 8.124038405 + -5 n = 8.124038405 + -5 Combine like terms: 8.124038405 + -5 = 3.124038405 n = 3.124038405 Simplifying n = 3.124038405

Subproblem 2

n + 5 = -8.124038405 Simplifying n + 5 = -8.124038405 Reorder the terms: 5 + n = -8.124038405 Solving 5 + n = -8.124038405 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 = -8.124038405 + -5 Combine like terms: 5 + -5 = 0 0 + n = -8.124038405 + -5 n = -8.124038405 + -5 Combine like terms: -8.124038405 + -5 = -13.124038405 n = -13.124038405 Simplifying n = -13.124038405

Solution

The solution to the problem is based on the solutions from the subproblems. n = {3.124038405, -13.124038405}

See similar equations:

| 2x-3+8=7(x-1-2x) | | 8x+17=48 | | 8x-17=48 | | 2x-3+8=7(x-7)-2x | | 28s+56=336 | | 2(2l+10)=52 | | 3(a-7)=30 | | 5x-3x-6=26 | | 2+(2x-8)=4618 | | f(x)=-9+2 | | 14x+24=5x+168 | | X=(60-X)+x | | -9y-6=4y+20 | | 1-2(-1)+0= | | k-7/6=8 | | 28=-8v+(v+6) | | 2x+2x+1+2x+2=14 | | 4+log[5](-2x)=5 | | 3p=13 | | -2a^0(x^6y^3z^2)-1/6x^4y^1z^3 | | 5A-10B=200 | | 5x^2-1000x+50000=0 | | 2a^0(x^6y^3z^2)-1/6x^4y^1z^3 | | (x/4)-1=-7 | | x/-5=0 | | 6x+y=5300 | | 3/18:11/27 | | f(77)=7/11p-10 | | 9x-4=5(2x-4) | | 35-(x/4)=x/3 | | 13-21x=7x+61 | | c^2+26x=68 |

Equations solver categories