n^2-3n-32=0

Simple and best practice solution for n^2-3n-32=0 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^2-3n-32=0 equation:


Simplifying
n2 + -3n + -32 = 0

Reorder the terms:
-32 + -3n + n2 = 0

Solving
-32 + -3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -3n + 32 + n2 = 0 + 32

Reorder the terms:
-32 + 32 + -3n + n2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -3n + n2 = 0 + 32
-3n + n2 = 0 + 32

Combine like terms: 0 + 32 = 32
-3n + n2 = 32

The n term is -3n.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3n + 2.25 + n2 = 32 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 32 + 2.25

Combine like terms: 32 + 2.25 = 34.25
2.25 + -3n + n2 = 34.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 34.25

Calculate the square root of the right side: 5.852349955

Break this problem into two subproblems by setting 
(n + -1.5) equal to 5.852349955 and -5.852349955.

Subproblem 1

n + -1.5 = 5.852349955 Simplifying n + -1.5 = 5.852349955 Reorder the terms: -1.5 + n = 5.852349955 Solving -1.5 + n = 5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = 5.852349955 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 5.852349955 + 1.5 n = 5.852349955 + 1.5 Combine like terms: 5.852349955 + 1.5 = 7.352349955 n = 7.352349955 Simplifying n = 7.352349955

Subproblem 2

n + -1.5 = -5.852349955 Simplifying n + -1.5 = -5.852349955 Reorder the terms: -1.5 + n = -5.852349955 Solving -1.5 + n = -5.852349955 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + n = -5.852349955 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -5.852349955 + 1.5 n = -5.852349955 + 1.5 Combine like terms: -5.852349955 + 1.5 = -4.352349955 n = -4.352349955 Simplifying n = -4.352349955

Solution

The solution to the problem is based on the solutions from the subproblems. n = {7.352349955, -4.352349955}

See similar equations:

| 5*4-20= | | 3/7x-6=8 | | 3p+5=2p+9 | | (1-3)^2/4*8+8-2^2 | | -3(8x-6)=3 | | 2(x+5)+105=7x-5(x-9) | | 0.4a-0.75b=c | | 4-9=-12 | | (1-5a)=29 | | 9x^2+3x-5=7x^2 | | -1.345*10^-5/1.578*10^8 | | (-4+5x)=16 | | (-2r-1)=11 | | X^2+20x-100=18 | | (-2r-1)=1 | | X^2+20x-10=18 | | X^2+20x+100=18 | | (-6m)=30 | | X^2+20x+10=18 | | (-3r)=9 | | 19.5/6.5 | | x^2-9=9x+1 | | (3x)=9 | | 13/y+5/y=2 | | 12x+5=13x-10 | | 3y+5/2=2y/3 | | 0.6666666= | | 7/15=r-14/15 | | 3/4p=9 | | -42+9x=10(2x+5)-4 | | y=3x/4+5 | | l-2=-10 |

Equations solver categories