21z^2+85z-21=0

Simple and best practice solution for 21z^2+85z-21=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 21z^2+85z-21=0 equation:


Simplifying
21z2 + 85z + -21 = 0

Reorder the terms:
-21 + 85z + 21z2 = 0

Solving
-21 + 85z + 21z2 = 0

Solving for variable 'z'.

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

Divide each side by '21'.
-1 + 4.047619048z + z2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4.047619048z + 1 + z2 = 0 + 1

Reorder the terms:
-1 + 1 + 4.047619048z + z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4.047619048z + z2 = 0 + 1
4.047619048z + z2 = 0 + 1

Combine like terms: 0 + 1 = 1
4.047619048z + z2 = 1

The z term is 4.047619048z.  Take half its coefficient (2.023809524).
Square it (4.095804989) and add it to both sides.

Add '4.095804989' to each side of the equation.
4.047619048z + 4.095804989 + z2 = 1 + 4.095804989

Reorder the terms:
4.095804989 + 4.047619048z + z2 = 1 + 4.095804989

Combine like terms: 1 + 4.095804989 = 5.095804989
4.095804989 + 4.047619048z + z2 = 5.095804989

Factor a perfect square on the left side:
(z + 2.023809524)(z + 2.023809524) = 5.095804989

Calculate the square root of the right side: 2.257388976

Break this problem into two subproblems by setting 
(z + 2.023809524) equal to 2.257388976 and -2.257388976.

Subproblem 1

z + 2.023809524 = 2.257388976 Simplifying z + 2.023809524 = 2.257388976 Reorder the terms: 2.023809524 + z = 2.257388976 Solving 2.023809524 + z = 2.257388976 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.023809524' to each side of the equation. 2.023809524 + -2.023809524 + z = 2.257388976 + -2.023809524 Combine like terms: 2.023809524 + -2.023809524 = 0.000000000 0.000000000 + z = 2.257388976 + -2.023809524 z = 2.257388976 + -2.023809524 Combine like terms: 2.257388976 + -2.023809524 = 0.233579452 z = 0.233579452 Simplifying z = 0.233579452

Subproblem 2

z + 2.023809524 = -2.257388976 Simplifying z + 2.023809524 = -2.257388976 Reorder the terms: 2.023809524 + z = -2.257388976 Solving 2.023809524 + z = -2.257388976 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-2.023809524' to each side of the equation. 2.023809524 + -2.023809524 + z = -2.257388976 + -2.023809524 Combine like terms: 2.023809524 + -2.023809524 = 0.000000000 0.000000000 + z = -2.257388976 + -2.023809524 z = -2.257388976 + -2.023809524 Combine like terms: -2.257388976 + -2.023809524 = -4.2811985 z = -4.2811985 Simplifying z = -4.2811985

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.233579452, -4.2811985}

See similar equations:

| 6(x+3)-1=26-3x-9+9x | | 9+x=95 | | 6v-7v=2 | | 6x-7=325 | | 6+3[4[2(7n-3)-6(4n+7)-3]+9n]=2-5[3(6n-2)+7] | | 2x^2-3x+101=360 | | F(x)=3x-5.3 | | (X+3)+(2x-5)=0 | | 8x-72=240 | | Ix+5I=3x-7 | | 3cos^2-cos-2=0 | | 5+14a=9a-5 | | X-4=5x+24 | | 3.7=9.1-.9x | | 274/5= | | 9x^7+15x^6+33X^4= | | 2+6g=11-3g | | 274*5= | | 36x^2-49x+4= | | 24x/5=5x-1 | | -4=14-3y | | 4.9=1.8-.4y | | -17-86= | | 5x/-2 | | 16.9=3n-1 | | 3(4x-2)=7(x+4) | | f(3)=6+6 | | X+57+90+40=180 | | 2x^2+2x+114=0 | | b-3/-5=5 | | 0.5(2x-3)+1.5=6 | | 50a^2-32a=0 |

Equations solver categories