z^2+16z+41=0

Simple and best practice solution for z^2+16z+41=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 z^2+16z+41=0 equation:


Simplifying
z2 + 16z + 41 = 0

Reorder the terms:
41 + 16z + z2 = 0

Solving
41 + 16z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + 16z + -41 + z2 = 0 + -41

Reorder the terms:
41 + -41 + 16z + z2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + 16z + z2 = 0 + -41
16z + z2 = 0 + -41

Combine like terms: 0 + -41 = -41
16z + z2 = -41

The z term is 16z.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16z + 64 + z2 = -41 + 64

Reorder the terms:
64 + 16z + z2 = -41 + 64

Combine like terms: -41 + 64 = 23
64 + 16z + z2 = 23

Factor a perfect square on the left side:
(z + 8)(z + 8) = 23

Calculate the square root of the right side: 4.795831523

Break this problem into two subproblems by setting 
(z + 8) equal to 4.795831523 and -4.795831523.

Subproblem 1

z + 8 = 4.795831523 Simplifying z + 8 = 4.795831523 Reorder the terms: 8 + z = 4.795831523 Solving 8 + z = 4.795831523 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = 4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + z = 4.795831523 + -8 z = 4.795831523 + -8 Combine like terms: 4.795831523 + -8 = -3.204168477 z = -3.204168477 Simplifying z = -3.204168477

Subproblem 2

z + 8 = -4.795831523 Simplifying z + 8 = -4.795831523 Reorder the terms: 8 + z = -4.795831523 Solving 8 + z = -4.795831523 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + z = -4.795831523 + -8 Combine like terms: 8 + -8 = 0 0 + z = -4.795831523 + -8 z = -4.795831523 + -8 Combine like terms: -4.795831523 + -8 = -12.795831523 z = -12.795831523 Simplifying z = -12.795831523

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-3.204168477, -12.795831523}

See similar equations:

| 4w-46=-3w+10 | | 3y-5x=x+18 | | 3x+1.2=12x+7-1.2 | | 2+4i=equation | | X/x-2=2/5 | | a*6a=384 | | 5/7x1/4 | | -384*a*6a=0 | | 3(d-8)-5=5(d+2)+1 | | -y=x^2+5x-4 | | 12x^2+4y=0 | | ((49-x^2)/3x^4)(7x/35-5x) | | 5x-y+8=x+12 | | 8x-3(x+8)=c+36 | | 6-x=3x-36 | | 3(2x+3)-1=22 | | x^2+10y=0 | | f(x)=x-770 | | 5-(8cosx/sin^2x)=0 | | X=5.3+1.3y | | X+1X-7=0 | | 15a^3b^3/20a4b4 | | x+2+5+x+2=39 | | (n+5)-(n-10)=1 | | N+5-n-10=1 | | az+bz+ay+by= | | 1.1X*600+0.8y*300=201000 | | 9(x-1.2)=8.1 | | x^6+x^3-56=0 | | 5x+8=3+6x-8 | | 660x+240y=201000 | | y=x^2-5x-10 |

Equations solver categories