n^2-3n-77=0

Simple and best practice solution for n^2-3n-77=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-77=0 equation:


Simplifying
n2 + -3n + -77 = 0

Reorder the terms:
-77 + -3n + n2 = 0

Solving
-77 + -3n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '77' to each side of the equation.
-77 + -3n + 77 + n2 = 0 + 77

Reorder the terms:
-77 + 77 + -3n + n2 = 0 + 77

Combine like terms: -77 + 77 = 0
0 + -3n + n2 = 0 + 77
-3n + n2 = 0 + 77

Combine like terms: 0 + 77 = 77
-3n + n2 = 77

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 = 77 + 2.25

Reorder the terms:
2.25 + -3n + n2 = 77 + 2.25

Combine like terms: 77 + 2.25 = 79.25
2.25 + -3n + n2 = 79.25

Factor a perfect square on the left side:
(n + -1.5)(n + -1.5) = 79.25

Calculate the square root of the right side: 8.902246907

Break this problem into two subproblems by setting 
(n + -1.5) equal to 8.902246907 and -8.902246907.

Subproblem 1

n + -1.5 = 8.902246907 Simplifying n + -1.5 = 8.902246907 Reorder the terms: -1.5 + n = 8.902246907 Solving -1.5 + n = 8.902246907 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 = 8.902246907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = 8.902246907 + 1.5 n = 8.902246907 + 1.5 Combine like terms: 8.902246907 + 1.5 = 10.402246907 n = 10.402246907 Simplifying n = 10.402246907

Subproblem 2

n + -1.5 = -8.902246907 Simplifying n + -1.5 = -8.902246907 Reorder the terms: -1.5 + n = -8.902246907 Solving -1.5 + n = -8.902246907 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 = -8.902246907 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + n = -8.902246907 + 1.5 n = -8.902246907 + 1.5 Combine like terms: -8.902246907 + 1.5 = -7.402246907 n = -7.402246907 Simplifying n = -7.402246907

Solution

The solution to the problem is based on the solutions from the subproblems. n = {10.402246907, -7.402246907}

See similar equations:

| 5(6-4r)=V+21 | | 5/9*(81-32) | | 1/2(n^2-3n-77)=0 | | 9+3=3x | | 3(4z^2-4+1)-11(2z-1)+10=0 | | 0.36m+1.2mp-mp^2=0 | | x+8-4*(x)=2*(1+3x) | | 5(x-6)=4(x+7) | | 3(3z^2-4+1)-11(2z-1)+10=0 | | 10(v+4)-2v=2(4v+3)-11 | | -4(r+3)=-58 | | p=3a+2+4c | | -3/2=-1/7v-2/3 | | (r^2s^4/3)^6 | | 0.009(x+3)=0.012x+0.006 | | 3*(x-3)+5-2x=2(6+x) | | 9(u-3)=5u-31 | | 6(3x+4)+7(x+4)=6 | | -0.3x+0.3=-1.2-0.5x | | 2.4x=3.6x | | 12-7(h+6)+8=14-8 | | 35x^2-50x/5x | | -9(t-6)-2(5-3t)=-4(t-5)+8 | | 2m^2+7m+22=0 | | 0.17y+0.04(y+5000)=1670 | | w^2-7w-9=0 | | (5y+3)-(y-2)= | | 5(x+4)-(5+7x)=-3x | | 4z+5=z-15 | | -2/7x=-8 | | 4(c-3)=4+3c | | 0.5(c+6)= |

Equations solver categories