z^2-14z=-17

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Solution for z^2-14z=-17 equation:


Simplifying
z2 + -14z = -17

Reorder the terms:
-14z + z2 = -17

Solving
-14z + z2 = -17

Solving for variable 'z'.

Reorder the terms:
17 + -14z + z2 = -17 + 17

Combine like terms: -17 + 17 = 0
17 + -14z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + -14z + -17 + z2 = 0 + -17

Reorder the terms:
17 + -17 + -14z + z2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -14z + z2 = 0 + -17
-14z + z2 = 0 + -17

Combine like terms: 0 + -17 = -17
-14z + z2 = -17

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 = -17 + 49

Reorder the terms:
49 + -14z + z2 = -17 + 49

Combine like terms: -17 + 49 = 32
49 + -14z + z2 = 32

Factor a perfect square on the left side:
(z + -7)(z + -7) = 32

Calculate the square root of the right side: 5.656854249

Break this problem into two subproblems by setting 
(z + -7) equal to 5.656854249 and -5.656854249.

Subproblem 1

z + -7 = 5.656854249 Simplifying z + -7 = 5.656854249 Reorder the terms: -7 + z = 5.656854249 Solving -7 + z = 5.656854249 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 = 5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + z = 5.656854249 + 7 z = 5.656854249 + 7 Combine like terms: 5.656854249 + 7 = 12.656854249 z = 12.656854249 Simplifying z = 12.656854249

Subproblem 2

z + -7 = -5.656854249 Simplifying z + -7 = -5.656854249 Reorder the terms: -7 + z = -5.656854249 Solving -7 + z = -5.656854249 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 = -5.656854249 + 7 Combine like terms: -7 + 7 = 0 0 + z = -5.656854249 + 7 z = -5.656854249 + 7 Combine like terms: -5.656854249 + 7 = 1.343145751 z = 1.343145751 Simplifying z = 1.343145751

Solution

The solution to the problem is based on the solutions from the subproblems. z = {12.656854249, 1.343145751}

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