k^2-19k+14=0

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Solution for k^2-19k+14=0 equation:


Simplifying
k2 + -19k + 14 = 0

Reorder the terms:
14 + -19k + k2 = 0

Solving
14 + -19k + k2 = 0

Solving for variable 'k'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -19k + -14 + k2 = 0 + -14

Reorder the terms:
14 + -14 + -19k + k2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -19k + k2 = 0 + -14
-19k + k2 = 0 + -14

Combine like terms: 0 + -14 = -14
-19k + k2 = -14

The k term is -19k.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19k + 90.25 + k2 = -14 + 90.25

Reorder the terms:
90.25 + -19k + k2 = -14 + 90.25

Combine like terms: -14 + 90.25 = 76.25
90.25 + -19k + k2 = 76.25

Factor a perfect square on the left side:
(k + -9.5)(k + -9.5) = 76.25

Calculate the square root of the right side: 8.732124598

Break this problem into two subproblems by setting 
(k + -9.5) equal to 8.732124598 and -8.732124598.

Subproblem 1

k + -9.5 = 8.732124598 Simplifying k + -9.5 = 8.732124598 Reorder the terms: -9.5 + k = 8.732124598 Solving -9.5 + k = 8.732124598 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + k = 8.732124598 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + k = 8.732124598 + 9.5 k = 8.732124598 + 9.5 Combine like terms: 8.732124598 + 9.5 = 18.232124598 k = 18.232124598 Simplifying k = 18.232124598

Subproblem 2

k + -9.5 = -8.732124598 Simplifying k + -9.5 = -8.732124598 Reorder the terms: -9.5 + k = -8.732124598 Solving -9.5 + k = -8.732124598 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + k = -8.732124598 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + k = -8.732124598 + 9.5 k = -8.732124598 + 9.5 Combine like terms: -8.732124598 + 9.5 = 0.767875402 k = 0.767875402 Simplifying k = 0.767875402

Solution

The solution to the problem is based on the solutions from the subproblems. k = {18.232124598, 0.767875402}

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