5z^2+z-1=0

Simple and best practice solution for 5z^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 5z^2+z-1=0 equation:


Simplifying
5z2 + z + -1 = 0

Reorder the terms:
-1 + z + 5z2 = 0

Solving
-1 + z + 5z2 = 0

Solving for variable 'z'.

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

Divide each side by '5'.
-0.2 + 0.2z + z2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + 0.2z + 0.2 + z2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + 0.2z + z2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + 0.2z + z2 = 0 + 0.2
0.2z + z2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
0.2z + z2 = 0.2

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.
0.2z + 0.25 + z2 = 0.2 + 0.25

Reorder the terms:
0.25 + 0.2z + z2 = 0.2 + 0.25

Combine like terms: 0.2 + 0.25 = 0.45
0.25 + 0.2z + z2 = 0.45

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 0.45

Calculate the square root of the right side: 0.670820393

Break this problem into two subproblems by setting 
(z + 0.5) equal to 0.670820393 and -0.670820393.

Subproblem 1

z + 0.5 = 0.670820393 Simplifying z + 0.5 = 0.670820393 Reorder the terms: 0.5 + z = 0.670820393 Solving 0.5 + z = 0.670820393 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 = 0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 0.670820393 + -0.5 z = 0.670820393 + -0.5 Combine like terms: 0.670820393 + -0.5 = 0.170820393 z = 0.170820393 Simplifying z = 0.170820393

Subproblem 2

z + 0.5 = -0.670820393 Simplifying z + 0.5 = -0.670820393 Reorder the terms: 0.5 + z = -0.670820393 Solving 0.5 + z = -0.670820393 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 = -0.670820393 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -0.670820393 + -0.5 z = -0.670820393 + -0.5 Combine like terms: -0.670820393 + -0.5 = -1.170820393 z = -1.170820393 Simplifying z = -1.170820393

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.170820393, -1.170820393}

See similar equations:

| 10x+30=20-8x+3x | | -16x^2+43x-22=0 | | -2y+7-3y=2 | | 4(10+7x)=292 | | 10y+16y+4=2y | | 120-4x=2yYequals | | (a+7)2=0 | | 6(1x+1)=54 | | -4(2x+6)=30+x | | 4x-5-8x=-38-3 | | 14x-6z=86 | | 186=-1+10b | | -3d-49=-7 | | 2=-6*-4 | | (-3)(12)=y | | 6x+6forx=32 | | 2x+4(x-4)=38 | | T-3.50=32.50 | | 7+12=-22 | | 5a-3a-4=10 | | 12x^2+18+6=0 | | 4x-2+2x=-74 | | 75-9g=5(-4g+2g) | | 3c+-4c+1=5c+2+3 | | -28=2+6x | | 9(n+2(n-20))=45 | | y/3=16 | | 3-6x=141 | | 2x+7=5-10 | | 5.83+m=21.83 | | 120=4x-2y | | -5x-31=13 |

Equations solver categories