z^2-10z=-22

Simple and best practice solution for z^2-10z=-22 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=-22 equation:


Simplifying
z2 + -10z = -22

Reorder the terms:
-10z + z2 = -22

Solving
-10z + z2 = -22

Solving for variable 'z'.

Reorder the terms:
22 + -10z + z2 = -22 + 22

Combine like terms: -22 + 22 = 0
22 + -10z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + -10z + -22 + z2 = 0 + -22

Reorder the terms:
22 + -22 + -10z + z2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -10z + z2 = 0 + -22
-10z + z2 = 0 + -22

Combine like terms: 0 + -22 = -22
-10z + z2 = -22

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 = -22 + 25

Reorder the terms:
25 + -10z + z2 = -22 + 25

Combine like terms: -22 + 25 = 3
25 + -10z + z2 = 3

Factor a perfect square on the left side:
(z + -5)(z + -5) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(z + -5) equal to 1.732050808 and -1.732050808.

Subproblem 1

z + -5 = 1.732050808 Simplifying z + -5 = 1.732050808 Reorder the terms: -5 + z = 1.732050808 Solving -5 + z = 1.732050808 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 = 1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + z = 1.732050808 + 5 z = 1.732050808 + 5 Combine like terms: 1.732050808 + 5 = 6.732050808 z = 6.732050808 Simplifying z = 6.732050808

Subproblem 2

z + -5 = -1.732050808 Simplifying z + -5 = -1.732050808 Reorder the terms: -5 + z = -1.732050808 Solving -5 + z = -1.732050808 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 = -1.732050808 + 5 Combine like terms: -5 + 5 = 0 0 + z = -1.732050808 + 5 z = -1.732050808 + 5 Combine like terms: -1.732050808 + 5 = 3.267949192 z = 3.267949192 Simplifying z = 3.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. z = {6.732050808, 3.267949192}

See similar equations:

| 5d-2=2d+4d | | 3=-7x+5x | | Y=-.67(0)+4 | | (3/4)x=(2/3)x-2/5 | | 130x-x=205 | | n+3=-12 | | Y=-.67(6)+4 | | 4x+25=71 | | X^2-9x-19/4=0 | | 9y+17=6y+38 | | -7+2x=-1x+5 | | 7x+12=-4+1+9x-5 | | 32+5(35)= | | 71x-4=25 | | 32+5(30)= | | 3x-6+11x= | | Y=1/8x | | 3y-2+y+30=7y+30-5y | | 32+5(25)= | | x+(x-30)+x=180 | | 32+5(20)= | | 5q+5=-2q+20 | | 32+5(15)= | | 6x+44-10x+65=180 | | 5n+8=3n-10 | | 32+5(10)= | | 8x+15(x+25)=720 | | 13x+6y=-48 | | 4a-16=1-15 | | 35/[4x(15-13)-3] | | 7x+4-(2x+8)=51 | | 300m+0.05=600m+0.01 |

Equations solver categories