k^2+9=7k

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Solution for k^2+9=7k equation:


Simplifying
k2 + 9 = 7k

Reorder the terms:
9 + k2 = 7k

Solving
9 + k2 = 7k

Solving for variable 'k'.

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

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

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -7k + -9 + k2 = 0 + -9

Reorder the terms:
9 + -9 + -7k + k2 = 0 + -9

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

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

The k term is -7k.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7k + 12.25 + k2 = -9 + 12.25

Reorder the terms:
12.25 + -7k + k2 = -9 + 12.25

Combine like terms: -9 + 12.25 = 3.25
12.25 + -7k + k2 = 3.25

Factor a perfect square on the left side:
(k + -3.5)(k + -3.5) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(k + -3.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

k + -3.5 = 1.802775638 Simplifying k + -3.5 = 1.802775638 Reorder the terms: -3.5 + k = 1.802775638 Solving -3.5 + k = 1.802775638 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = 1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = 1.802775638 + 3.5 k = 1.802775638 + 3.5 Combine like terms: 1.802775638 + 3.5 = 5.302775638 k = 5.302775638 Simplifying k = 5.302775638

Subproblem 2

k + -3.5 = -1.802775638 Simplifying k + -3.5 = -1.802775638 Reorder the terms: -3.5 + k = -1.802775638 Solving -3.5 + k = -1.802775638 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = -1.802775638 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = -1.802775638 + 3.5 k = -1.802775638 + 3.5 Combine like terms: -1.802775638 + 3.5 = 1.697224362 k = 1.697224362 Simplifying k = 1.697224362

Solution

The solution to the problem is based on the solutions from the subproblems. k = {5.302775638, 1.697224362}

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