16z^2-16z+2=0

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


Simplifying
16z2 + -16z + 2 = 0

Reorder the terms:
2 + -16z + 16z2 = 0

Solving
2 + -16z + 16z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + -8z + 8z2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -8z + 8z2)' equal to zero and attempt to solve:

Simplifying
1 + -8z + 8z2 = 0

Solving
1 + -8z + 8z2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
0.125 + -1z + z2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + -1z + -0.125 + z2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + -1z + z2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + -1z + z2 = 0 + -0.125
-1z + z2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
-1z + z2 = -0.125

The z term is -1z.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1z + 0.25 + z2 = -0.125 + 0.25

Reorder the terms:
0.25 + -1z + z2 = -0.125 + 0.25

Combine like terms: -0.125 + 0.25 = 0.125
0.25 + -1z + z2 = 0.125

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 0.125

Calculate the square root of the right side: 0.353553391

Break this problem into two subproblems by setting 
(z + -0.5) equal to 0.353553391 and -0.353553391.


Subproblem 1
z + -0.5 = 0.353553391

Simplifying
z + -0.5 = 0.353553391

Reorder the terms:
-0.5 + z = 0.353553391

Solving
-0.5 + z = 0.353553391

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = 0.353553391 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = 0.353553391 + 0.5
z = 0.353553391 + 0.5

Combine like terms: 0.353553391 + 0.5 = 0.853553391
z = 0.853553391

Simplifying
z = 0.853553391


Subproblem 2
z + -0.5 = -0.353553391

Simplifying
z + -0.5 = -0.353553391

Reorder the terms:
-0.5 + z = -0.353553391

Solving
-0.5 + z = -0.353553391

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + z = -0.353553391 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + z = -0.353553391 + 0.5
z = -0.353553391 + 0.5

Combine like terms: -0.353553391 + 0.5 = 0.146446609
z = 0.146446609

Simplifying
z = 0.146446609


Solution
The solution to the problem is based on the solutions
from the subproblems.
z = {0.853553391, 0.146446609}
Solution
z = {0.853553391, 0.146446609}

See similar equations:

| -x/2=-1 | | 6(8-3n)=-32-2n | | (-x/-x+4)+9=6x/x-4 | | 8+3(p-4)=2p+2(p+1) | | 6x+24y=0 | | p^2=-18p-80 | | aX+4Y=M | | [x-16]+5=-15 | | x^2+8x+61=0 | | 12x-(x-1)=11+4x | | 7x+8=10x-8 | | 39.50x=18762.50 | | 5(5x+2)-3(2x-4)=45 | | H(h)=6h+4h+1 | | 39.50x=177750 | | 5-(2m+13)=-3m | | y=2/3x+10 | | 5x+y=18-2x | | -2x-3x+8=8-5x-20 | | 9x-18x-6-16x^2=0 | | x(1+5)=x(2-7)+2 | | 7(x-2)=4(x+15) | | 120*2=p(4*6) | | 12x^2+10x+12=0 | | -16t^2+1936=0 | | 5x^2+20x+25=5 | | z^4-16i=0 | | 36y^2+y-44=0 | | 9=x(3) | | x+3/t=t2 | | 12x-5x+8x= | | 2x+1/3=-3 |

Equations solver categories