z^2+2z=64

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Solution for z^2+2z=64 equation:


Simplifying
z2 + 2z = 64

Reorder the terms:
2z + z2 = 64

Solving
2z + z2 = 64

Solving for variable 'z'.

Reorder the terms:
-64 + 2z + z2 = 64 + -64

Combine like terms: 64 + -64 = 0
-64 + 2z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '64' to each side of the equation.
-64 + 2z + 64 + z2 = 0 + 64

Reorder the terms:
-64 + 64 + 2z + z2 = 0 + 64

Combine like terms: -64 + 64 = 0
0 + 2z + z2 = 0 + 64
2z + z2 = 0 + 64

Combine like terms: 0 + 64 = 64
2z + z2 = 64

The z term is 2z.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2z + 1 + z2 = 64 + 1

Reorder the terms:
1 + 2z + z2 = 64 + 1

Combine like terms: 64 + 1 = 65
1 + 2z + z2 = 65

Factor a perfect square on the left side:
(z + 1)(z + 1) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(z + 1) equal to 8.062257748 and -8.062257748.

Subproblem 1

z + 1 = 8.062257748 Simplifying z + 1 = 8.062257748 Reorder the terms: 1 + z = 8.062257748 Solving 1 + z = 8.062257748 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = 8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + z = 8.062257748 + -1 z = 8.062257748 + -1 Combine like terms: 8.062257748 + -1 = 7.062257748 z = 7.062257748 Simplifying z = 7.062257748

Subproblem 2

z + 1 = -8.062257748 Simplifying z + 1 = -8.062257748 Reorder the terms: 1 + z = -8.062257748 Solving 1 + z = -8.062257748 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + z = -8.062257748 + -1 Combine like terms: 1 + -1 = 0 0 + z = -8.062257748 + -1 z = -8.062257748 + -1 Combine like terms: -8.062257748 + -1 = -9.062257748 z = -9.062257748 Simplifying z = -9.062257748

Solution

The solution to the problem is based on the solutions from the subproblems. z = {7.062257748, -9.062257748}

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