z(z+9)=1

Simple and best practice solution for z(z+9)=1 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(z+9)=1 equation:


Simplifying
z(z + 9) = 1

Reorder the terms:
z(9 + z) = 1
(9 * z + z * z) = 1
(9z + z2) = 1

Solving
9z + z2 = 1

Solving for variable 'z'.

Reorder the terms:
-1 + 9z + z2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 9z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 9z + 1 + z2 = 0 + 1

Reorder the terms:
-1 + 1 + 9z + z2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 9z + z2 = 0 + 1
9z + z2 = 0 + 1

Combine like terms: 0 + 1 = 1
9z + z2 = 1

The z term is 9z.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9z + 20.25 + z2 = 1 + 20.25

Reorder the terms:
20.25 + 9z + z2 = 1 + 20.25

Combine like terms: 1 + 20.25 = 21.25
20.25 + 9z + z2 = 21.25

Factor a perfect square on the left side:
(z + 4.5)(z + 4.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(z + 4.5) equal to 4.609772229 and -4.609772229.

Subproblem 1

z + 4.5 = 4.609772229 Simplifying z + 4.5 = 4.609772229 Reorder the terms: 4.5 + z = 4.609772229 Solving 4.5 + z = 4.609772229 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = 4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = 4.609772229 + -4.5 z = 4.609772229 + -4.5 Combine like terms: 4.609772229 + -4.5 = 0.109772229 z = 0.109772229 Simplifying z = 0.109772229

Subproblem 2

z + 4.5 = -4.609772229 Simplifying z + 4.5 = -4.609772229 Reorder the terms: 4.5 + z = -4.609772229 Solving 4.5 + z = -4.609772229 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + z = -4.609772229 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + z = -4.609772229 + -4.5 z = -4.609772229 + -4.5 Combine like terms: -4.609772229 + -4.5 = -9.109772229 z = -9.109772229 Simplifying z = -9.109772229

Solution

The solution to the problem is based on the solutions from the subproblems. z = {0.109772229, -9.109772229}

See similar equations:

| Cx-4=dx+9 | | f(x)=(2x^2)-20x+54 | | -3*3+2=3 | | 10-(x-1)=8x-3+7x | | 3(h+9)=4 | | K^2+5x-14=0 | | X+X+9+3X= | | (x)(x)+5x= | | X-28+x+12=180 | | 4m+4m=5m+3 | | 7x^6-21x^5=0 | | 4+3x-3=7 | | a+13=2a-13 | | 0.16x+0.20(5-x)=0.9 | | n+(2n-9)+(3n+6)=123 | | 19.95-0.55=95.30 | | 8(m+7)=9m | | 8x-3=-75 | | 3(6z-1)2(z+3)=14(z+1) | | f(x)=20+0.15x | | (x^14)6= | | 5x+6x-20=80-9x | | -9=-7r-2r | | F(X)=7+4x | | x+2=-1-x | | 4x-9+2x+27=90 | | 7(3b-4)= | | 8+x=-7x-16 | | a+bi=34+14i | | 6x+16-15x=-1 | | 6p=2p+13 | | -0.1x^2+20x-750=0 |

Equations solver categories