z^2-14z=46

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Solution for z^2-14z=46 equation:


Simplifying
z2 + -14z = 46

Reorder the terms:
-14z + z2 = 46

Solving
-14z + z2 = 46

Solving for variable 'z'.

Reorder the terms:
-46 + -14z + z2 = 46 + -46

Combine like terms: 46 + -46 = 0
-46 + -14z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + -14z + 46 + z2 = 0 + 46

Reorder the terms:
-46 + 46 + -14z + z2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -14z + z2 = 0 + 46
-14z + z2 = 0 + 46

Combine like terms: 0 + 46 = 46
-14z + z2 = 46

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 = 46 + 49

Reorder the terms:
49 + -14z + z2 = 46 + 49

Combine like terms: 46 + 49 = 95
49 + -14z + z2 = 95

Factor a perfect square on the left side:
(z + -7)(z + -7) = 95

Calculate the square root of the right side: 9.746794345

Break this problem into two subproblems by setting 
(z + -7) equal to 9.746794345 and -9.746794345.

Subproblem 1

z + -7 = 9.746794345 Simplifying z + -7 = 9.746794345 Reorder the terms: -7 + z = 9.746794345 Solving -7 + z = 9.746794345 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 = 9.746794345 + 7 Combine like terms: -7 + 7 = 0 0 + z = 9.746794345 + 7 z = 9.746794345 + 7 Combine like terms: 9.746794345 + 7 = 16.746794345 z = 16.746794345 Simplifying z = 16.746794345

Subproblem 2

z + -7 = -9.746794345 Simplifying z + -7 = -9.746794345 Reorder the terms: -7 + z = -9.746794345 Solving -7 + z = -9.746794345 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 = -9.746794345 + 7 Combine like terms: -7 + 7 = 0 0 + z = -9.746794345 + 7 z = -9.746794345 + 7 Combine like terms: -9.746794345 + 7 = -2.746794345 z = -2.746794345 Simplifying z = -2.746794345

Solution

The solution to the problem is based on the solutions from the subproblems. z = {16.746794345, -2.746794345}

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