z^2+26z=43

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Solution for z^2+26z=43 equation:


Simplifying
z2 + 26z = 43

Reorder the terms:
26z + z2 = 43

Solving
26z + z2 = 43

Solving for variable 'z'.

Reorder the terms:
-43 + 26z + z2 = 43 + -43

Combine like terms: 43 + -43 = 0
-43 + 26z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + 26z + 43 + z2 = 0 + 43

Reorder the terms:
-43 + 43 + 26z + z2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 26z + z2 = 0 + 43
26z + z2 = 0 + 43

Combine like terms: 0 + 43 = 43
26z + z2 = 43

The z term is 26z.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26z + 169 + z2 = 43 + 169

Reorder the terms:
169 + 26z + z2 = 43 + 169

Combine like terms: 43 + 169 = 212
169 + 26z + z2 = 212

Factor a perfect square on the left side:
(z + 13)(z + 13) = 212

Calculate the square root of the right side: 14.560219779

Break this problem into two subproblems by setting 
(z + 13) equal to 14.560219779 and -14.560219779.

Subproblem 1

z + 13 = 14.560219779 Simplifying z + 13 = 14.560219779 Reorder the terms: 13 + z = 14.560219779 Solving 13 + z = 14.560219779 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + z = 14.560219779 + -13 Combine like terms: 13 + -13 = 0 0 + z = 14.560219779 + -13 z = 14.560219779 + -13 Combine like terms: 14.560219779 + -13 = 1.560219779 z = 1.560219779 Simplifying z = 1.560219779

Subproblem 2

z + 13 = -14.560219779 Simplifying z + 13 = -14.560219779 Reorder the terms: 13 + z = -14.560219779 Solving 13 + z = -14.560219779 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + z = -14.560219779 + -13 Combine like terms: 13 + -13 = 0 0 + z = -14.560219779 + -13 z = -14.560219779 + -13 Combine like terms: -14.560219779 + -13 = -27.560219779 z = -27.560219779 Simplifying z = -27.560219779

Solution

The solution to the problem is based on the solutions from the subproblems. z = {1.560219779, -27.560219779}

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