z^2+8z+4=

Simple and best practice solution for z^2+8z+4= 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+8z+4= equation:


Simplifying
z2 + 8z + 4 = 0

Reorder the terms:
4 + 8z + z2 = 0

Solving
4 + 8z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 8z + -4 + z2 = 0 + -4

Reorder the terms:
4 + -4 + 8z + z2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 8z + z2 = 0 + -4
8z + z2 = 0 + -4

Combine like terms: 0 + -4 = -4
8z + z2 = -4

The z term is 8z.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8z + 16 + z2 = -4 + 16

Reorder the terms:
16 + 8z + z2 = -4 + 16

Combine like terms: -4 + 16 = 12
16 + 8z + z2 = 12

Factor a perfect square on the left side:
(z + 4)(z + 4) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(z + 4) equal to 3.464101615 and -3.464101615.

Subproblem 1

z + 4 = 3.464101615 Simplifying z + 4 = 3.464101615 Reorder the terms: 4 + z = 3.464101615 Solving 4 + z = 3.464101615 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = 3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + z = 3.464101615 + -4 z = 3.464101615 + -4 Combine like terms: 3.464101615 + -4 = -0.535898385 z = -0.535898385 Simplifying z = -0.535898385

Subproblem 2

z + 4 = -3.464101615 Simplifying z + 4 = -3.464101615 Reorder the terms: 4 + z = -3.464101615 Solving 4 + z = -3.464101615 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + z = -3.464101615 + -4 Combine like terms: 4 + -4 = 0 0 + z = -3.464101615 + -4 z = -3.464101615 + -4 Combine like terms: -3.464101615 + -4 = -7.464101615 z = -7.464101615 Simplifying z = -7.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.535898385, -7.464101615}

See similar equations:

| 2x+60=360 | | x^2-10x+7=0 | | 15b^2-53b-28=0 | | -2x-4=8x+5 | | 5x-13=2x-4 | | (2n-5)+(m-2)=3-7 | | 4x^21+32=0 | | 2m+(3n+1)-6=8 | | 2d^3+4d= | | 2n^2-9n-126=0 | | (7-y)(3y-5)=0 | | 8(7+4a)-3(5+2b)=0 | | 34+15w=3w-w+4w | | -5=9(x-3)-3x | | 7x+9=57+x | | -8-x=-3x-6 | | 4x+5=3x+12 | | 15=20x | | n^2-11n+28=0 | | 8e-1=2 | | 4g-11=7 | | 3(2x+3)-4x=-3 | | 10x^2-28x-6=0 | | 9x+24=8 | | -6x-4=-7x+11 | | 12x-10y=2 | | 8(7+4a)-3(5+2b)=990 | | -7x+6=-8x+14 | | 0.25=[0.25*(r+1)-1] | | 2x-1=6x+15 | | 2(4-x+2x)=12 | | 26=3x-2-7x |

Equations solver categories