z^2-z-50=0

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Solution for z^2-z-50=0 equation:


Simplifying
z2 + -1z + -50 = 0

Reorder the terms:
-50 + -1z + z2 = 0

Solving
-50 + -1z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -1z + 50 + z2 = 0 + 50

Reorder the terms:
-50 + 50 + -1z + z2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1z + z2 = 0 + 50
-1z + z2 = 0 + 50

Combine like terms: 0 + 50 = 50
-1z + z2 = 50

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 = 50 + 0.25

Reorder the terms:
0.25 + -1z + z2 = 50 + 0.25

Combine like terms: 50 + 0.25 = 50.25
0.25 + -1z + z2 = 50.25

Factor a perfect square on the left side:
(z + -0.5)(z + -0.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(z + -0.5) equal to 7.088723439 and -7.088723439.

Subproblem 1

z + -0.5 = 7.088723439 Simplifying z + -0.5 = 7.088723439 Reorder the terms: -0.5 + z = 7.088723439 Solving -0.5 + z = 7.088723439 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 = 7.088723439 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = 7.088723439 + 0.5 z = 7.088723439 + 0.5 Combine like terms: 7.088723439 + 0.5 = 7.588723439 z = 7.588723439 Simplifying z = 7.588723439

Subproblem 2

z + -0.5 = -7.088723439 Simplifying z + -0.5 = -7.088723439 Reorder the terms: -0.5 + z = -7.088723439 Solving -0.5 + z = -7.088723439 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 = -7.088723439 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + z = -7.088723439 + 0.5 z = -7.088723439 + 0.5 Combine like terms: -7.088723439 + 0.5 = -6.588723439 z = -6.588723439 Simplifying z = -6.588723439

Solution

The solution to the problem is based on the solutions from the subproblems. z = {7.588723439, -6.588723439}

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