z^2+z=144

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Solution for z^2+z=144 equation:


Simplifying
z2 + z = 144

Reorder the terms:
z + z2 = 144

Solving
z + z2 = 144

Solving for variable 'z'.

Reorder the terms:
-144 + z + z2 = 144 + -144

Combine like terms: 144 + -144 = 0
-144 + z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '144' to each side of the equation.
-144 + z + 144 + z2 = 0 + 144

Reorder the terms:
-144 + 144 + z + z2 = 0 + 144

Combine like terms: -144 + 144 = 0
0 + z + z2 = 0 + 144
z + z2 = 0 + 144

Combine like terms: 0 + 144 = 144
z + z2 = 144

The z term is z.  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.
z + 0.25 + z2 = 144 + 0.25

Reorder the terms:
0.25 + z + z2 = 144 + 0.25

Combine like terms: 144 + 0.25 = 144.25
0.25 + z + z2 = 144.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = 144.25

Calculate the square root of the right side: 12.010412149

Break this problem into two subproblems by setting 
(z + 0.5) equal to 12.010412149 and -12.010412149.

Subproblem 1

z + 0.5 = 12.010412149 Simplifying z + 0.5 = 12.010412149 Reorder the terms: 0.5 + z = 12.010412149 Solving 0.5 + z = 12.010412149 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 = 12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = 12.010412149 + -0.5 z = 12.010412149 + -0.5 Combine like terms: 12.010412149 + -0.5 = 11.510412149 z = 11.510412149 Simplifying z = 11.510412149

Subproblem 2

z + 0.5 = -12.010412149 Simplifying z + 0.5 = -12.010412149 Reorder the terms: 0.5 + z = -12.010412149 Solving 0.5 + z = -12.010412149 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 = -12.010412149 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + z = -12.010412149 + -0.5 z = -12.010412149 + -0.5 Combine like terms: -12.010412149 + -0.5 = -12.510412149 z = -12.510412149 Simplifying z = -12.510412149

Solution

The solution to the problem is based on the solutions from the subproblems. z = {11.510412149, -12.510412149}

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