z^2-18z=-19

Simple and best practice solution for z^2-18z=-19 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^2-18z=-19 equation:


Simplifying
z2 + -18z = -19

Reorder the terms:
-18z + z2 = -19

Solving
-18z + z2 = -19

Solving for variable 'z'.

Reorder the terms:
19 + -18z + z2 = -19 + 19

Combine like terms: -19 + 19 = 0
19 + -18z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-19' to each side of the equation.
19 + -18z + -19 + z2 = 0 + -19

Reorder the terms:
19 + -19 + -18z + z2 = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -18z + z2 = 0 + -19
-18z + z2 = 0 + -19

Combine like terms: 0 + -19 = -19
-18z + z2 = -19

The z term is -18z.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18z + 81 + z2 = -19 + 81

Reorder the terms:
81 + -18z + z2 = -19 + 81

Combine like terms: -19 + 81 = 62
81 + -18z + z2 = 62

Factor a perfect square on the left side:
(z + -9)(z + -9) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(z + -9) equal to 7.874007874 and -7.874007874.

Subproblem 1

z + -9 = 7.874007874 Simplifying z + -9 = 7.874007874 Reorder the terms: -9 + z = 7.874007874 Solving -9 + z = 7.874007874 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = 7.874007874 + 9 Combine like terms: -9 + 9 = 0 0 + z = 7.874007874 + 9 z = 7.874007874 + 9 Combine like terms: 7.874007874 + 9 = 16.874007874 z = 16.874007874 Simplifying z = 16.874007874

Subproblem 2

z + -9 = -7.874007874 Simplifying z + -9 = -7.874007874 Reorder the terms: -9 + z = -7.874007874 Solving -9 + z = -7.874007874 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + z = -7.874007874 + 9 Combine like terms: -9 + 9 = 0 0 + z = -7.874007874 + 9 z = -7.874007874 + 9 Combine like terms: -7.874007874 + 9 = 1.125992126 z = 1.125992126 Simplifying z = 1.125992126

Solution

The solution to the problem is based on the solutions from the subproblems. z = {16.874007874, 1.125992126}

See similar equations:

| 78+e=185 | | 50+(2x+10)=90 | | s^2+5s=-20 | | 1+1-2*3+8-5= | | 4w^2+7w=194 | | 4x^7/3 | | x+x+3x=0 | | x^2+15x=4 | | 12b^2+26b+12=0 | | 16x^3y^2-(3x^2z-5x^3y^2)+6x^2z= | | 4y+3=2y+18 | | (x^2-3x-10)/(x-5) | | 3b^2-12b=0 | | (x^2-3x-10)/x-5 | | 2+x(0.4771)=2x(0.9542) | | 9x+2x-6y=29+1 | | (2x+9)(X)=240 | | 8x+9x-3=69+1 | | 38x+20y=150 | | 2-sin*2x=4*sin*2x | | g^2+g=306 | | 6y^4=3y^3 | | 15y=72+y | | 5(3n+1)=7(4n+8)+1 | | 9(2n+1)=8(8n+9)+5 | | -X^3-3x^2+2x-4=0 | | 43(x+14)=774 | | (15m/18x)/(20m/3x) | | 16u-9u=28 | | 8y=7x+10 | | 0.02(y-6)+0.10y=0.06y-0.6 | | 4m=-24+7m |

Equations solver categories