z^2=18+z

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


Simplifying
z2 = 18 + z

Solving
z2 = 18 + z

Solving for variable 'z'.

Reorder the terms:
-18 + -1z + z2 = 18 + z + -18 + -1z

Reorder the terms:
-18 + -1z + z2 = 18 + -18 + z + -1z

Combine like terms: 18 + -18 = 0
-18 + -1z + z2 = 0 + z + -1z
-18 + -1z + z2 = z + -1z

Combine like terms: z + -1z = 0
-18 + -1z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -1z + 18 + z2 = 0 + 18

Reorder the terms:
-18 + 18 + -1z + z2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1z + z2 = 0 + 18
-1z + z2 = 0 + 18

Combine like terms: 0 + 18 = 18
-1z + z2 = 18

The z term is -1z.  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.
-1z + 0.25 + z2 = 18 + 0.25

Reorder the terms:
0.25 + -1z + z2 = 18 + 0.25

Combine like terms: 18 + 0.25 = 18.25
0.25 + -1z + z2 = 18.25

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(z + -0.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

z + -0.5 = 4.272001873 Simplifying z + -0.5 = 4.272001873 Reorder the terms: -0.5 + z = 4.272001873 Solving -0.5 + z = 4.272001873 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 = 4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 4.272001873 + 0.5 z = 4.272001873 + 0.5 Combine like terms: 4.272001873 + 0.5 = 4.772001873 z = 4.772001873 Simplifying z = 4.772001873

Subproblem 2

z + -0.5 = -4.272001873 Simplifying z + -0.5 = -4.272001873 Reorder the terms: -0.5 + z = -4.272001873 Solving -0.5 + z = -4.272001873 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 = -4.272001873 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -4.272001873 + 0.5 z = -4.272001873 + 0.5 Combine like terms: -4.272001873 + 0.5 = -3.772001873 z = -3.772001873 Simplifying z = -3.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. z = {4.772001873, -3.772001873}

See similar equations:

| 16x-1=3(x+5) | | 5x^2+10x+20-7=0 | | 550-330+280-140= | | 24x^2+81x+27= | | -2(49-3)=30 | | 5(3x-5)+2(18-4x)-2(3x+4)=-6 | | ln(5x)=(lnx^2) | | -4-4w=5-5x | | H-j=k | | H-j=kforj | | 4w-4=6w-6 | | -1x=-4 | | 3y^3-11y^2=3y^2+24y | | 10x-1=(2x+1)(2x+1) | | ln(7x)=2ln(6x) | | 2u-4=-4u+20 | | -18+(-8)= | | .5-3d=2 | | .5d+3=2 | | 7t+4=14t-5 | | 3r=14+10r | | 15n+3-19n= | | (2x-5)(3x-7)= | | 12p+5+3p-5= | | -(3+X)+2-3X=-17 | | x+9=4whatisx | | x+5=-8whatisx | | 1+r^2=1.25 | | x+-9=-3whatisx | | 27=-7x | | 6x-10x+20=0 | | 5(q-7)-3(2q-4)+25=0 |

Equations solver categories