-4z^2+z+1=0

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


Simplifying
-4z2 + z + 1 = 0

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

Solving
1 + z + -4z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-0.25 + -0.25z + z2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.25z + 0.25 + z2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.25z + z2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.25z + z2 = 0 + 0.25
-0.25z + z2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.25z + z2 = 0.25

The z term is z.  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.
-0.25z + 0.25 + z2 = 0.25 + 0.25

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

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

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

Calculate the square root of the right side: 0.707106781

Break this problem into two subproblems by setting 
(z + 0.5) equal to 0.707106781 and -0.707106781.

Subproblem 1

z + 0.5 = 0.707106781 Simplifying z + 0.5 = 0.707106781 Reorder the terms: 0.5 + z = 0.707106781 Solving 0.5 + z = 0.707106781 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 = 0.707106781 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 0.707106781 + -0.5 z = 0.707106781 + -0.5 Combine like terms: 0.707106781 + -0.5 = 0.207106781 z = 0.207106781 Simplifying z = 0.207106781

Subproblem 2

z + 0.5 = -0.707106781 Simplifying z + 0.5 = -0.707106781 Reorder the terms: 0.5 + z = -0.707106781 Solving 0.5 + z = -0.707106781 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 = -0.707106781 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -0.707106781 + -0.5 z = -0.707106781 + -0.5 Combine like terms: -0.707106781 + -0.5 = -1.207106781 z = -1.207106781 Simplifying z = -1.207106781

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.207106781, -1.207106781}

See similar equations:

| 7(4-x)=-14 | | 6x+5x+3x=3x-13 | | 71m-62m+3=-31m | | 5(x-2)=3(x-8) | | 4=17t-16t^2 | | 8(x+3)=6x-18 | | x^2-8x=x(8+x) | | 4w^2+1090w-13020=0 | | 3r^3+18r^2=81r | | 10+3x=31 | | 68x+65x= | | 68x+68x= | | 20x+15=17+3 | | .75x^2+.5x-.5=0 | | 5x-1=5+3x | | x(3x-4)=-1 | | 3(3x-4)=-1 | | 19+19=5x-7 | | 19-5x-7= | | -5(4z-1)-4(z+9)=2(z+1) | | 9+6x=51 | | 14x+5+35=180 | | Y=2x^2+3x-2 | | 14x+5+35=360 | | 14x+5+35= | | -5(4z-1)-3(z+5)=2(z+1) | | X+13+21=180 | | X+13+21= | | 2y^2+8y-6=y^2+6y+9 | | X+15=x+15 | | 80+11x-10=180 | | -12-3x=0 |

Equations solver categories