4k^2-3k-11=0

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Solution for 4k^2-3k-11=0 equation:


Simplifying
4k2 + -3k + -11 = 0

Reorder the terms:
-11 + -3k + 4k2 = 0

Solving
-11 + -3k + 4k2 = 0

Solving for variable 'k'.

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

Divide each side by '4'.
-2.75 + -0.75k + k2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -0.75k + 2.75 + k2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -0.75k + k2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -0.75k + k2 = 0 + 2.75
-0.75k + k2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-0.75k + k2 = 2.75

The k term is -0.75k.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75k + 0.140625 + k2 = 2.75 + 0.140625

Reorder the terms:
0.140625 + -0.75k + k2 = 2.75 + 0.140625

Combine like terms: 2.75 + 0.140625 = 2.890625
0.140625 + -0.75k + k2 = 2.890625

Factor a perfect square on the left side:
(k + -0.375)(k + -0.375) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(k + -0.375) equal to 1.700183814 and -1.700183814.

Subproblem 1

k + -0.375 = 1.700183814 Simplifying k + -0.375 = 1.700183814 Reorder the terms: -0.375 + k = 1.700183814 Solving -0.375 + k = 1.700183814 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + k = 1.700183814 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + k = 1.700183814 + 0.375 k = 1.700183814 + 0.375 Combine like terms: 1.700183814 + 0.375 = 2.075183814 k = 2.075183814 Simplifying k = 2.075183814

Subproblem 2

k + -0.375 = -1.700183814 Simplifying k + -0.375 = -1.700183814 Reorder the terms: -0.375 + k = -1.700183814 Solving -0.375 + k = -1.700183814 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + k = -1.700183814 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + k = -1.700183814 + 0.375 k = -1.700183814 + 0.375 Combine like terms: -1.700183814 + 0.375 = -1.325183814 k = -1.325183814 Simplifying k = -1.325183814

Solution

The solution to the problem is based on the solutions from the subproblems. k = {2.075183814, -1.325183814}

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