7k^2-13=-9k

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Solution for 7k^2-13=-9k equation:


Simplifying
7k2 + -13 = -9k

Reorder the terms:
-13 + 7k2 = -9k

Solving
-13 + 7k2 = -9k

Solving for variable 'k'.

Reorder the terms:
-13 + 9k + 7k2 = -9k + 9k

Combine like terms: -9k + 9k = 0
-13 + 9k + 7k2 = 0

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

Divide each side by '7'.
-1.857142857 + 1.285714286k + k2 = 0

Move the constant term to the right:

Add '1.857142857' to each side of the equation.
-1.857142857 + 1.285714286k + 1.857142857 + k2 = 0 + 1.857142857

Reorder the terms:
-1.857142857 + 1.857142857 + 1.285714286k + k2 = 0 + 1.857142857

Combine like terms: -1.857142857 + 1.857142857 = 0.000000000
0.000000000 + 1.285714286k + k2 = 0 + 1.857142857
1.285714286k + k2 = 0 + 1.857142857

Combine like terms: 0 + 1.857142857 = 1.857142857
1.285714286k + k2 = 1.857142857

The k term is 1.285714286k.  Take half its coefficient (0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
1.285714286k + 0.4132653063 + k2 = 1.857142857 + 0.4132653063

Reorder the terms:
0.4132653063 + 1.285714286k + k2 = 1.857142857 + 0.4132653063

Combine like terms: 1.857142857 + 0.4132653063 = 2.2704081633
0.4132653063 + 1.285714286k + k2 = 2.2704081633

Factor a perfect square on the left side:
(k + 0.642857143)(k + 0.642857143) = 2.2704081633

Calculate the square root of the right side: 1.506787365

Break this problem into two subproblems by setting 
(k + 0.642857143) equal to 1.506787365 and -1.506787365.

Subproblem 1

k + 0.642857143 = 1.506787365 Simplifying k + 0.642857143 = 1.506787365 Reorder the terms: 0.642857143 + k = 1.506787365 Solving 0.642857143 + k = 1.506787365 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + k = 1.506787365 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + k = 1.506787365 + -0.642857143 k = 1.506787365 + -0.642857143 Combine like terms: 1.506787365 + -0.642857143 = 0.863930222 k = 0.863930222 Simplifying k = 0.863930222

Subproblem 2

k + 0.642857143 = -1.506787365 Simplifying k + 0.642857143 = -1.506787365 Reorder the terms: 0.642857143 + k = -1.506787365 Solving 0.642857143 + k = -1.506787365 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.642857143' to each side of the equation. 0.642857143 + -0.642857143 + k = -1.506787365 + -0.642857143 Combine like terms: 0.642857143 + -0.642857143 = 0.000000000 0.000000000 + k = -1.506787365 + -0.642857143 k = -1.506787365 + -0.642857143 Combine like terms: -1.506787365 + -0.642857143 = -2.149644508 k = -2.149644508 Simplifying k = -2.149644508

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.863930222, -2.149644508}

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