.60z(z-300)+.05z=.70z-205

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Solution for .60z(z-300)+.05z=.70z-205 equation:


Simplifying
0.60z(z + -300) + 0.05z = 0.70z + -205

Reorder the terms:
0.60z(-300 + z) + 0.05z = 0.70z + -205
(-300 * 0.60z + z * 0.60z) + 0.05z = 0.70z + -205
(-180z + 0.60z2) + 0.05z = 0.70z + -205

Reorder the terms:
-180z + 0.05z + 0.60z2 = 0.70z + -205

Combine like terms: -180z + 0.05z = -179.95z
-179.95z + 0.60z2 = 0.70z + -205

Reorder the terms:
-179.95z + 0.60z2 = -205 + 0.70z

Solving
-179.95z + 0.60z2 = -205 + 0.70z

Solving for variable 'z'.

Reorder the terms:
205 + -179.95z + -0.70z + 0.60z2 = -205 + 0.70z + 205 + -0.70z

Combine like terms: -179.95z + -0.70z = -180.65z
205 + -180.65z + 0.60z2 = -205 + 0.70z + 205 + -0.70z

Reorder the terms:
205 + -180.65z + 0.60z2 = -205 + 205 + 0.70z + -0.70z

Combine like terms: -205 + 205 = 0
205 + -180.65z + 0.60z2 = 0 + 0.70z + -0.70z
205 + -180.65z + 0.60z2 = 0.70z + -0.70z

Combine like terms: 0.70z + -0.70z = 0.00
205 + -180.65z + 0.60z2 = 0.00

Begin completing the square.  Divide all terms by
0.60 the coefficient of the squared term: 

Divide each side by '0.60'.
341.6666667 + -301.0833333z + z2 = 0

Move the constant term to the right:

Add '-341.6666667' to each side of the equation.
341.6666667 + -301.0833333z + -341.6666667 + z2 = 0 + -341.6666667

Reorder the terms:
341.6666667 + -341.6666667 + -301.0833333z + z2 = 0 + -341.6666667

Combine like terms: 341.6666667 + -341.6666667 = 0.0000000
0.0000000 + -301.0833333z + z2 = 0 + -341.6666667
-301.0833333z + z2 = 0 + -341.6666667

Combine like terms: 0 + -341.6666667 = -341.6666667
-301.0833333z + z2 = -341.6666667

The z term is -301.0833333z.  Take half its coefficient (-150.5416667).
Square it (22662.79341) and add it to both sides.

Add '22662.79341' to each side of the equation.
-301.0833333z + 22662.79341 + z2 = -341.6666667 + 22662.79341

Reorder the terms:
22662.79341 + -301.0833333z + z2 = -341.6666667 + 22662.79341

Combine like terms: -341.6666667 + 22662.79341 = 22321.1267433
22662.79341 + -301.0833333z + z2 = 22321.1267433

Factor a perfect square on the left side:
(z + -150.5416667)(z + -150.5416667) = 22321.1267433

Calculate the square root of the right side: 149.402566053

Break this problem into two subproblems by setting 
(z + -150.5416667) equal to 149.402566053 and -149.402566053.

Subproblem 1

z + -150.5416667 = 149.402566053 Simplifying z + -150.5416667 = 149.402566053 Reorder the terms: -150.5416667 + z = 149.402566053 Solving -150.5416667 + z = 149.402566053 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '150.5416667' to each side of the equation. -150.5416667 + 150.5416667 + z = 149.402566053 + 150.5416667 Combine like terms: -150.5416667 + 150.5416667 = 0.0000000 0.0000000 + z = 149.402566053 + 150.5416667 z = 149.402566053 + 150.5416667 Combine like terms: 149.402566053 + 150.5416667 = 299.944232753 z = 299.944232753 Simplifying z = 299.944232753

Subproblem 2

z + -150.5416667 = -149.402566053 Simplifying z + -150.5416667 = -149.402566053 Reorder the terms: -150.5416667 + z = -149.402566053 Solving -150.5416667 + z = -149.402566053 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '150.5416667' to each side of the equation. -150.5416667 + 150.5416667 + z = -149.402566053 + 150.5416667 Combine like terms: -150.5416667 + 150.5416667 = 0.0000000 0.0000000 + z = -149.402566053 + 150.5416667 z = -149.402566053 + 150.5416667 Combine like terms: -149.402566053 + 150.5416667 = 1.139100647 z = 1.139100647 Simplifying z = 1.139100647

Solution

The solution to the problem is based on the solutions from the subproblems. z = {299.944232753, 1.139100647}

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