n^2-3n-84=0

Simple and best practice solution for n^2-3n-84=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-84=0 equation:


Simplifying
n2 + -3n + -84 = 0

Reorder the terms:
-84 + -3n + n2 = 0

Solving
-84 + -3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -3n + 84 + n2 = 0 + 84

Reorder the terms:
-84 + 84 + -3n + n2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -3n + n2 = 0 + 84
-3n + n2 = 0 + 84

Combine like terms: 0 + 84 = 84
-3n + n2 = 84

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 = 84 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 84 + 2.25

Combine like terms: 84 + 2.25 = 86.25
2.25 + -3n + n2 = 86.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 86.25

Calculate the square root of the right side: 9.287087811

Break this problem into two subproblems by setting 
(n + -1.5) equal to 9.287087811 and -9.287087811.

Subproblem 1

n + -1.5 = 9.287087811 Simplifying n + -1.5 = 9.287087811 Reorder the terms: -1.5 + n = 9.287087811 Solving -1.5 + n = 9.287087811 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 = 9.287087811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 9.287087811 + 1.5 n = 9.287087811 + 1.5 Combine like terms: 9.287087811 + 1.5 = 10.787087811 n = 10.787087811 Simplifying n = 10.787087811

Subproblem 2

n + -1.5 = -9.287087811 Simplifying n + -1.5 = -9.287087811 Reorder the terms: -1.5 + n = -9.287087811 Solving -1.5 + n = -9.287087811 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 = -9.287087811 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -9.287087811 + 1.5 n = -9.287087811 + 1.5 Combine like terms: -9.287087811 + 1.5 = -7.787087811 n = -7.787087811 Simplifying n = -7.787087811

Solution

The solution to the problem is based on the solutions from the subproblems. n = {10.787087811, -7.787087811}

See similar equations:

| -12y-3x=57 | | 2x-2=10x-56 | | 2(2x+1)=1 | | x+y=31 | | z=x | | 12y-3x=57 | | 4x^3+2x^2-30x=0 | | 8(y-1)(y+3)=5(y-2)(y+1) | | -12x-3x=57 | | x^2+x^2+2x+1-61= | | -9=m-9 | | 2(4x+1)=5(3x-2) | | .08(7x-1.2)-.08=.2(-1.2x+.05) | | 8x+12=15x | | -3n-2=4 | | 4(x-9)-(3x+5)=-2 | | 2x^2+80=2.849 | | 35w-5xw+49-7x=0 | | 24-5t-t^2=0 | | 2(x-1)-(3x-3)=4x | | 3x^2+9x-50=0 | | 3(5x+2)+10=2(4x-5)+7x+6 | | -5(z-7)-(6z-9)=-12 | | (2e^3x)+1=9 | | xw+2x-3w-6=0 | | 0=24-36a-24a^2 | | 5b-3=2b-9 | | 2w^2+11w+15=0 | | 5z^2+17z+14=0 | | (x-16)2=20 | | 100x+100= | | (x+7)2=-18 |

Equations solver categories