z^2=-45-15z

Simple and best practice solution for z^2=-45-15z 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=-45-15z equation:


Simplifying
z2 = -45 + -15z

Solving
z2 = -45 + -15z

Solving for variable 'z'.

Reorder the terms:
45 + 15z + z2 = -45 + -15z + 45 + 15z

Reorder the terms:
45 + 15z + z2 = -45 + 45 + -15z + 15z

Combine like terms: -45 + 45 = 0
45 + 15z + z2 = 0 + -15z + 15z
45 + 15z + z2 = -15z + 15z

Combine like terms: -15z + 15z = 0
45 + 15z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + 15z + -45 + z2 = 0 + -45

Reorder the terms:
45 + -45 + 15z + z2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + 15z + z2 = 0 + -45
15z + z2 = 0 + -45

Combine like terms: 0 + -45 = -45
15z + z2 = -45

The z term is 15z.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15z + 56.25 + z2 = -45 + 56.25

Reorder the terms:
56.25 + 15z + z2 = -45 + 56.25

Combine like terms: -45 + 56.25 = 11.25
56.25 + 15z + z2 = 11.25

Factor a perfect square on the left side:
(z + 7.5)(z + 7.5) = 11.25

Calculate the square root of the right side: 3.354101966

Break this problem into two subproblems by setting 
(z + 7.5) equal to 3.354101966 and -3.354101966.

Subproblem 1

z + 7.5 = 3.354101966 Simplifying z + 7.5 = 3.354101966 Reorder the terms: 7.5 + z = 3.354101966 Solving 7.5 + z = 3.354101966 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + z = 3.354101966 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + z = 3.354101966 + -7.5 z = 3.354101966 + -7.5 Combine like terms: 3.354101966 + -7.5 = -4.145898034 z = -4.145898034 Simplifying z = -4.145898034

Subproblem 2

z + 7.5 = -3.354101966 Simplifying z + 7.5 = -3.354101966 Reorder the terms: 7.5 + z = -3.354101966 Solving 7.5 + z = -3.354101966 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + z = -3.354101966 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + z = -3.354101966 + -7.5 z = -3.354101966 + -7.5 Combine like terms: -3.354101966 + -7.5 = -10.854101966 z = -10.854101966 Simplifying z = -10.854101966

Solution

The solution to the problem is based on the solutions from the subproblems. z = {-4.145898034, -10.854101966}

See similar equations:

| 3(x-5)+14X=18X+5 | | 3(x-5)+14X=18XB+5 | | 4-4-4/4 | | ((((x/2)/3)/4)/5)=6 | | (-18)(2)/(-6)(-1) | | 1/8n-7=-1/4n-13 | | -16/-1-4-3 | | 13-4x=-43 | | 99x=99y+297 | | 8x+11x-9x=-10+16x-3x+4 | | 5r-41=34-4r | | (-4)(15/5-2) | | m+5(m-1)=17 | | 11y+22x=88 | | p^3+1/8p^3 | | 8m+35=-51 | | ln(3+x)=0 | | 9/4-(-2+3) | | 6/6-4+2 | | 5/11n=3 | | 16x+6=26-24 | | 2m^2=162 | | -r/3=-101 | | -6/6-(-5)(2) | | 10=a/-2 | | w/4=-80 | | x/2=98 | | (-5+8)4= | | 4x^(-2/3)+8x^(1/3) | | 3m-2n-4(3m-2n)= | | f(x)=-6x-x | | 40x+6(1.5x)=660 |

Equations solver categories