n^2-4n-19=0

Simple and best practice solution for n^2-4n-19=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^2-4n-19=0 equation:


Simplifying
n2 + -4n + -19 = 0

Reorder the terms:
-19 + -4n + n2 = 0

Solving
-19 + -4n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + -4n + 19 + n2 = 0 + 19

Reorder the terms:
-19 + 19 + -4n + n2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -4n + n2 = 0 + 19
-4n + n2 = 0 + 19

Combine like terms: 0 + 19 = 19
-4n + n2 = 19

The n term is -4n.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4n + 4 + n2 = 19 + 4

Reorder the terms:
4 + -4n + n2 = 19 + 4

Combine like terms: 19 + 4 = 23
4 + -4n + n2 = 23

Factor a perfect square on the left side:
(n + -2)(n + -2) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(n + -2) equal to 4.795831523 and -4.795831523.

Subproblem 1

n + -2 = 4.795831523 Simplifying n + -2 = 4.795831523 Reorder the terms: -2 + n = 4.795831523 Solving -2 + n = 4.795831523 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = 4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + n = 4.795831523 + 2 n = 4.795831523 + 2 Combine like terms: 4.795831523 + 2 = 6.795831523 n = 6.795831523 Simplifying n = 6.795831523

Subproblem 2

n + -2 = -4.795831523 Simplifying n + -2 = -4.795831523 Reorder the terms: -2 + n = -4.795831523 Solving -2 + n = -4.795831523 Solving for variable 'n'. Move all terms containing n to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + n = -4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + n = -4.795831523 + 2 n = -4.795831523 + 2 Combine like terms: -4.795831523 + 2 = -2.795831523 n = -2.795831523 Simplifying n = -2.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. n = {6.795831523, -2.795831523}

See similar equations:

| (2x-1)/21=(3x-7)/15 | | 6x+5-5x=11-20 | | x^2+8x-5x-40=0 | | 18v^9x^7-24v^3x^2y^4=0 | | 2x+10i=1 | | 2(x+4)+6=-9.7 | | 4x^2+7x-20=0 | | x(x+10)-13(x+10)=0 | | 7logx=14 | | 2x^2-3x-32=-48 | | 9x-8x^3=0 | | 10y^2+4y^3=0 | | 8y^2-16y+40=0 | | 7c+3c+3=6+4c | | 35/4(x^(3/2))-70=0 | | x+5x+6x=8 | | 35/4(x^(3/2))-70 | | 5x+15x^2=0 | | 11m^3-12m^2=0 | | 0.074/5 | | 16b+20b^3=0 | | 4x-1=2x+14 | | 6x-y=90/30 | | (-5k^2/2k^5)/((2k)^3/10k^5) | | 4a-15a^3=0 | | 3(x+5)-7-x=36 | | 5/8•2/3 | | 16x^2+8x-7=0 | | 5(x+4)-3(x-2)= | | 460=200x | | 2cos^3(x)-cosx=(cos^2(x)-sin^2(x))/secx | | 2(6)+y=7 |

Equations solver categories