-z^2-14z+43=0

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Solution for -z^2-14z+43=0 equation:


Simplifying
-1z2 + -14z + 43 = 0

Reorder the terms:
43 + -14z + -1z2 = 0

Solving
43 + -14z + -1z2 = 0

Solving for variable 'z'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-43 + 14z + z2 = 0

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + 14z + 43 + z2 = 0 + 43

Reorder the terms:
-43 + 43 + 14z + z2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 14z + z2 = 0 + 43
14z + z2 = 0 + 43

Combine like terms: 0 + 43 = 43
14z + z2 = 43

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 = 43 + 49

Reorder the terms:
49 + 14z + z2 = 43 + 49

Combine like terms: 43 + 49 = 92
49 + 14z + z2 = 92

Factor a perfect square on the left side:
(z + 7)(z + 7) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(z + 7) equal to 9.591663047 and -9.591663047.

Subproblem 1

z + 7 = 9.591663047 Simplifying z + 7 = 9.591663047 Reorder the terms: 7 + z = 9.591663047 Solving 7 + z = 9.591663047 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 = 9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + z = 9.591663047 + -7 z = 9.591663047 + -7 Combine like terms: 9.591663047 + -7 = 2.591663047 z = 2.591663047 Simplifying z = 2.591663047

Subproblem 2

z + 7 = -9.591663047 Simplifying z + 7 = -9.591663047 Reorder the terms: 7 + z = -9.591663047 Solving 7 + z = -9.591663047 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 = -9.591663047 + -7 Combine like terms: 7 + -7 = 0 0 + z = -9.591663047 + -7 z = -9.591663047 + -7 Combine like terms: -9.591663047 + -7 = -16.591663047 z = -16.591663047 Simplifying z = -16.591663047

Solution

The solution to the problem is based on the solutions from the subproblems. z = {2.591663047, -16.591663047}

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