z^2-13z=20

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Solution for z^2-13z=20 equation:


Simplifying
z2 + -13z = 20

Reorder the terms:
-13z + z2 = 20

Solving
-13z + z2 = 20

Solving for variable 'z'.

Reorder the terms:
-20 + -13z + z2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + -13z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -13z + 20 + z2 = 0 + 20

Reorder the terms:
-20 + 20 + -13z + z2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -13z + z2 = 0 + 20
-13z + z2 = 0 + 20

Combine like terms: 0 + 20 = 20
-13z + z2 = 20

The z term is -13z.  Take half its coefficient (-6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
-13z + 42.25 + z2 = 20 + 42.25

Reorder the terms:
42.25 + -13z + z2 = 20 + 42.25

Combine like terms: 20 + 42.25 = 62.25
42.25 + -13z + z2 = 62.25

Factor a perfect square on the left side:
(z + -6.5)(z + -6.5) = 62.25

Calculate the square root of the right side: 7.889866919

Break this problem into two subproblems by setting 
(z + -6.5) equal to 7.889866919 and -7.889866919.

Subproblem 1

z + -6.5 = 7.889866919 Simplifying z + -6.5 = 7.889866919 Reorder the terms: -6.5 + z = 7.889866919 Solving -6.5 + z = 7.889866919 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + z = 7.889866919 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + z = 7.889866919 + 6.5 z = 7.889866919 + 6.5 Combine like terms: 7.889866919 + 6.5 = 14.389866919 z = 14.389866919 Simplifying z = 14.389866919

Subproblem 2

z + -6.5 = -7.889866919 Simplifying z + -6.5 = -7.889866919 Reorder the terms: -6.5 + z = -7.889866919 Solving -6.5 + z = -7.889866919 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + z = -7.889866919 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + z = -7.889866919 + 6.5 z = -7.889866919 + 6.5 Combine like terms: -7.889866919 + 6.5 = -1.389866919 z = -1.389866919 Simplifying z = -1.389866919

Solution

The solution to the problem is based on the solutions from the subproblems. z = {14.389866919, -1.389866919}

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