2z^2-4z^2+2z+1=0

Simple and best practice solution for 2z^2-4z^2+2z+1=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 2z^2-4z^2+2z+1=0 equation:


Simplifying
2z2 + -4z2 + 2z + 1 = 0

Reorder the terms:
1 + 2z + 2z2 + -4z2 = 0

Combine like terms: 2z2 + -4z2 = -2z2
1 + 2z + -2z2 = 0

Solving
1 + 2z + -2z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-0.5 + -1z + z2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -1z + 0.5 + z2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -1z + z2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -1z + z2 = 0 + 0.5
-1z + z2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-1z + z2 = 0.5

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 = 0.5 + 0.25

Reorder the terms:
0.25 + -1z + z2 = 0.5 + 0.25

Combine like terms: 0.5 + 0.25 = 0.75
0.25 + -1z + z2 = 0.75

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 0.75

Calculate the square root of the right side: 0.866025404

Break this problem into two subproblems by setting 
(z + -0.5) equal to 0.866025404 and -0.866025404.

Subproblem 1

z + -0.5 = 0.866025404 Simplifying z + -0.5 = 0.866025404 Reorder the terms: -0.5 + z = 0.866025404 Solving -0.5 + z = 0.866025404 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 = 0.866025404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 0.866025404 + 0.5 z = 0.866025404 + 0.5 Combine like terms: 0.866025404 + 0.5 = 1.366025404 z = 1.366025404 Simplifying z = 1.366025404

Subproblem 2

z + -0.5 = -0.866025404 Simplifying z + -0.5 = -0.866025404 Reorder the terms: -0.5 + z = -0.866025404 Solving -0.5 + z = -0.866025404 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 = -0.866025404 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -0.866025404 + 0.5 z = -0.866025404 + 0.5 Combine like terms: -0.866025404 + 0.5 = -0.366025404 z = -0.366025404 Simplifying z = -0.366025404

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.366025404, -0.366025404}

See similar equations:

| (8/2g-14) | | 5+6ln(x)=13 | | 6(x-4)-8x=30 | | 100X+500=1000 | | 5+6lnx=13 | | k-2/5=m | | 337=22q+51 | | 27x-10=3x+20 | | 16x^2-a^2-2a-1=0 | | x=y(z+n) | | (6-1y)+(1+4y)=43 | | (6-1)+(1+4y)=43 | | 2(2x-4.9)=9x-9.8 | | 9u+9v-4(6u-3v)= | | ab+bc-ad-bd=0 | | 14x=12x-4 | | 3.6x-32=2.6x+3 | | 21x^4/3x^-1 | | 16(135/360)= | | x+3y=3200 | | R(x)=50-5x^2/3 | | 1.0x=29 | | 3(n-2)-19=5+2(n+2) | | 2sin^2(3x)-1=0 | | 3x-2+2=6 | | sqrt(2t-1)+sqrt(3t+3)=5 | | 88=7v+18 | | 0=(6-2x)(6-6x) | | 1.3x+4-4.3x=7 | | t/d-a/d=1 | | 3x^2-11x=101 | | xlogy+8xy=24 |

Equations solver categories