z^2=10z-20

Simple and best practice solution for z^2=10z-20 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 z^2=10z-20 equation:


Simplifying
z2 = 10z + -20

Reorder the terms:
z2 = -20 + 10z

Solving
z2 = -20 + 10z

Solving for variable 'z'.

Reorder the terms:
20 + -10z + z2 = -20 + 10z + 20 + -10z

Reorder the terms:
20 + -10z + z2 = -20 + 20 + 10z + -10z

Combine like terms: -20 + 20 = 0
20 + -10z + z2 = 0 + 10z + -10z
20 + -10z + z2 = 10z + -10z

Combine like terms: 10z + -10z = 0
20 + -10z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-20' to each side of the equation.
20 + -10z + -20 + z2 = 0 + -20

Reorder the terms:
20 + -20 + -10z + z2 = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -10z + z2 = 0 + -20
-10z + z2 = 0 + -20

Combine like terms: 0 + -20 = -20
-10z + z2 = -20

The z term is -10z.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10z + 25 + z2 = -20 + 25

Reorder the terms:
25 + -10z + z2 = -20 + 25

Combine like terms: -20 + 25 = 5
25 + -10z + z2 = 5

Factor a perfect square on the left side:
(z + -5)(z + -5) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(z + -5) equal to 2.236067978 and -2.236067978.

Subproblem 1

z + -5 = 2.236067978 Simplifying z + -5 = 2.236067978 Reorder the terms: -5 + z = 2.236067978 Solving -5 + z = 2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = 2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + z = 2.236067978 + 5 z = 2.236067978 + 5 Combine like terms: 2.236067978 + 5 = 7.236067978 z = 7.236067978 Simplifying z = 7.236067978

Subproblem 2

z + -5 = -2.236067978 Simplifying z + -5 = -2.236067978 Reorder the terms: -5 + z = -2.236067978 Solving -5 + z = -2.236067978 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + z = -2.236067978 + 5 Combine like terms: -5 + 5 = 0 0 + z = -2.236067978 + 5 z = -2.236067978 + 5 Combine like terms: -2.236067978 + 5 = 2.763932022 z = 2.763932022 Simplifying z = 2.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. z = {7.236067978, 2.763932022}

See similar equations:

| 8x+100=10x | | .8x+.05(14-x)=.10(-98) | | z^2-10z=-20 | | z^2-10x=-20 | | 3x=2x+20 | | .8x+.05(14-x)=.10x(-98) | | z^2-10z=20 | | -18=x-4 | | .8x+.05x(14-x)=.10x(-98) | | n^2=-10n-25 | | 4x+11=3x+36 | | z^2-22z+21=0 | | .8x+.5x(14-x)=.10x(-98) | | -83=17-4x | | (X^2)+(9x)+14=0 | | 5m+2m=21 | | 31-3y=41 | | 29r-13=57 | | x^3-37x-84=0 | | 28w-56=-8 | | 54y-13=17.8 | | 8a^3-26a^2+15a= | | 12x+18=9x+51 | | 15a+8a^3-26a^2= | | 5x=21 | | 24t=-6(8-4t) | | -3y-7=-6 | | 5x=20-5 | | x^2+12x+26=10 | | 9-5(2x+10)=-1 | | 13x+4=10x+10 | | 2p-4=5p+5 |

Equations solver categories