4k^2-5k-4=0

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Solution for 4k^2-5k-4=0 equation:


Simplifying
4k2 + -5k + -4 = 0

Reorder the terms:
-4 + -5k + 4k2 = 0

Solving
-4 + -5k + 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'.
-1 + -1.25k + k2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.25k + 1 + k2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.25k + k2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.25k + k2 = 0 + 1
-1.25k + k2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.25k + k2 = 1

The k term is -1.25k.  Take half its coefficient (-0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
-1.25k + 0.390625 + k2 = 1 + 0.390625

Reorder the terms:
0.390625 + -1.25k + k2 = 1 + 0.390625

Combine like terms: 1 + 0.390625 = 1.390625
0.390625 + -1.25k + k2 = 1.390625

Factor a perfect square on the left side:
(k + -0.625)(k + -0.625) = 1.390625

Calculate the square root of the right side: 1.179247642

Break this problem into two subproblems by setting 
(k + -0.625) equal to 1.179247642 and -1.179247642.

Subproblem 1

k + -0.625 = 1.179247642 Simplifying k + -0.625 = 1.179247642 Reorder the terms: -0.625 + k = 1.179247642 Solving -0.625 + k = 1.179247642 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + k = 1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + k = 1.179247642 + 0.625 k = 1.179247642 + 0.625 Combine like terms: 1.179247642 + 0.625 = 1.804247642 k = 1.804247642 Simplifying k = 1.804247642

Subproblem 2

k + -0.625 = -1.179247642 Simplifying k + -0.625 = -1.179247642 Reorder the terms: -0.625 + k = -1.179247642 Solving -0.625 + k = -1.179247642 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + k = -1.179247642 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + k = -1.179247642 + 0.625 k = -1.179247642 + 0.625 Combine like terms: -1.179247642 + 0.625 = -0.554247642 k = -0.554247642 Simplifying k = -0.554247642

Solution

The solution to the problem is based on the solutions from the subproblems. k = {1.804247642, -0.554247642}

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