z^2-14z-13=0

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Solution for z^2-14z-13=0 equation:


Simplifying
z2 + -14z + -13 = 0

Reorder the terms:
-13 + -14z + z2 = 0

Solving
-13 + -14z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -14z + 13 + z2 = 0 + 13

Reorder the terms:
-13 + 13 + -14z + z2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -14z + z2 = 0 + 13
-14z + z2 = 0 + 13

Combine like terms: 0 + 13 = 13
-14z + z2 = 13

The z term is -14z.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14z + 49 + z2 = 13 + 49

Reorder the terms:
49 + -14z + z2 = 13 + 49

Combine like terms: 13 + 49 = 62
49 + -14z + z2 = 62

Factor a perfect square on the left side:
(z + -7)(z + -7) = 62

Calculate the square root of the right side: 7.874007874

Break this problem into two subproblems by setting 
(z + -7) equal to 7.874007874 and -7.874007874.

Subproblem 1

z + -7 = 7.874007874 Simplifying z + -7 = 7.874007874 Reorder the terms: -7 + z = 7.874007874 Solving -7 + z = 7.874007874 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = 7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + z = 7.874007874 + 7 z = 7.874007874 + 7 Combine like terms: 7.874007874 + 7 = 14.874007874 z = 14.874007874 Simplifying z = 14.874007874

Subproblem 2

z + -7 = -7.874007874 Simplifying z + -7 = -7.874007874 Reorder the terms: -7 + z = -7.874007874 Solving -7 + z = -7.874007874 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + z = -7.874007874 + 7 Combine like terms: -7 + 7 = 0 0 + z = -7.874007874 + 7 z = -7.874007874 + 7 Combine like terms: -7.874007874 + 7 = -0.874007874 z = -0.874007874 Simplifying z = -0.874007874

Solution

The solution to the problem is based on the solutions from the subproblems. z = {14.874007874, -0.874007874}

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