z^2+16z+7=0

Simple and best practice solution for z^2+16z+7=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+7=0 equation:


Simplifying
z2 + 16z + 7 = 0

Reorder the terms:
7 + 16z + z2 = 0

Solving
7 + 16z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 16z + -7 + z2 = 0 + -7

Reorder the terms:
7 + -7 + 16z + z2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 16z + z2 = 0 + -7
16z + z2 = 0 + -7

Combine like terms: 0 + -7 = -7
16z + z2 = -7

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 = -7 + 64

Reorder the terms:
64 + 16z + z2 = -7 + 64

Combine like terms: -7 + 64 = 57
64 + 16z + z2 = 57

Factor a perfect square on the left side:
(z + 8)(z + 8) = 57

Calculate the square root of the right side: 7.549834435

Break this problem into two subproblems by setting 
(z + 8) equal to 7.549834435 and -7.549834435.

Subproblem 1

z + 8 = 7.549834435 Simplifying z + 8 = 7.549834435 Reorder the terms: 8 + z = 7.549834435 Solving 8 + z = 7.549834435 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 = 7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + z = 7.549834435 + -8 z = 7.549834435 + -8 Combine like terms: 7.549834435 + -8 = -0.450165565 z = -0.450165565 Simplifying z = -0.450165565

Subproblem 2

z + 8 = -7.549834435 Simplifying z + 8 = -7.549834435 Reorder the terms: 8 + z = -7.549834435 Solving 8 + z = -7.549834435 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 = -7.549834435 + -8 Combine like terms: 8 + -8 = 0 0 + z = -7.549834435 + -8 z = -7.549834435 + -8 Combine like terms: -7.549834435 + -8 = -15.549834435 z = -15.549834435 Simplifying z = -15.549834435

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-0.450165565, -15.549834435}

See similar equations:

| X+3y+3z=10 | | x/x^2=0 | | (Ab+b-c+6)+(3ab-b+c-6)= | | 8a-4(-5a-2)=24a | | 6u+8=21 | | 2y-24=26 | | 1/3s=-2 | | 10-2/5x=-3 | | 5e+6pd+5d-7ed+7= | | 10-2/5x=3 | | 1/2(13f/5 | | 4-1/2v=-4 | | 2.5+-3.5x=-32x+-48 | | 4-1/2v=4 | | 12+4pd-2p+6pd= | | -5w^3-4w^2=7w+16 | | 2.5+-3.5x=-32+-48 | | 8-5n=3.25 | | -3yx+2x+6y-4=0 | | 5x-9=54-4x | | 2x+3y+4x+5x+6x= | | 2x+2x-6=8 | | P+pq-q-p+3pq-3-q+7= | | 6m^2+23m+15=0 | | (-5r-4)(-r-6)= | | (k-1)x^2-2x+2k=0 | | 12/w=3 | | 7y-80=xy-6x | | (4x^5)^2/2X^12 | | 18k+29=11k-11y | | 2x+x-5+100=360 | | 2x+x-5+100=90 |

Equations solver categories