-2+k=7-20k^2

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Solution for -2+k=7-20k^2 equation:


Simplifying
-2 + k = 7 + -20k2

Solving
-2 + k = 7 + -20k2

Solving for variable 'k'.

Reorder the terms:
-2 + -7 + k + 20k2 = 7 + -20k2 + -7 + 20k2

Combine like terms: -2 + -7 = -9
-9 + k + 20k2 = 7 + -20k2 + -7 + 20k2

Reorder the terms:
-9 + k + 20k2 = 7 + -7 + -20k2 + 20k2

Combine like terms: 7 + -7 = 0
-9 + k + 20k2 = 0 + -20k2 + 20k2
-9 + k + 20k2 = -20k2 + 20k2

Combine like terms: -20k2 + 20k2 = 0
-9 + k + 20k2 = 0

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

Divide each side by '20'.
-0.45 + 0.05k + k2 = 0

Move the constant term to the right:

Add '0.45' to each side of the equation.
-0.45 + 0.05k + 0.45 + k2 = 0 + 0.45

Reorder the terms:
-0.45 + 0.45 + 0.05k + k2 = 0 + 0.45

Combine like terms: -0.45 + 0.45 = 0.00
0.00 + 0.05k + k2 = 0 + 0.45
0.05k + k2 = 0 + 0.45

Combine like terms: 0 + 0.45 = 0.45
0.05k + k2 = 0.45

The k term is k.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.05k + 0.25 + k2 = 0.45 + 0.25

Reorder the terms:
0.25 + 0.05k + k2 = 0.45 + 0.25

Combine like terms: 0.45 + 0.25 = 0.7
0.25 + 0.05k + k2 = 0.7

Factor a perfect square on the left side:
(k + 0.5)(k + 0.5) = 0.7

Calculate the square root of the right side: 0.836660027

Break this problem into two subproblems by setting 
(k + 0.5) equal to 0.836660027 and -0.836660027.

Subproblem 1

k + 0.5 = 0.836660027 Simplifying k + 0.5 = 0.836660027 Reorder the terms: 0.5 + k = 0.836660027 Solving 0.5 + k = 0.836660027 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = 0.836660027 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = 0.836660027 + -0.5 k = 0.836660027 + -0.5 Combine like terms: 0.836660027 + -0.5 = 0.336660027 k = 0.336660027 Simplifying k = 0.336660027

Subproblem 2

k + 0.5 = -0.836660027 Simplifying k + 0.5 = -0.836660027 Reorder the terms: 0.5 + k = -0.836660027 Solving 0.5 + k = -0.836660027 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + k = -0.836660027 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + k = -0.836660027 + -0.5 k = -0.836660027 + -0.5 Combine like terms: -0.836660027 + -0.5 = -1.336660027 k = -1.336660027 Simplifying k = -1.336660027

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.336660027, -1.336660027}

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