2k^2+6k-2=0

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Solution for 2k^2+6k-2=0 equation:


Simplifying
2k2 + 6k + -2 = 0

Reorder the terms:
-2 + 6k + 2k2 = 0

Solving
-2 + 6k + 2k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1 + 3k + k2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-1 + 3k + k2)' equal to zero and attempt to solve: Simplifying -1 + 3k + k2 = 0 Solving -1 + 3k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + 3k + 1 + k2 = 0 + 1 Reorder the terms: -1 + 1 + 3k + k2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3k + k2 = 0 + 1 3k + k2 = 0 + 1 Combine like terms: 0 + 1 = 1 3k + k2 = 1 The k term is 3k. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3k + 2.25 + k2 = 1 + 2.25 Reorder the terms: 2.25 + 3k + k2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + 3k + k2 = 3.25 Factor a perfect square on the left side: (k + 1.5)(k + 1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (k + 1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

k + 1.5 = 1.802775638 Simplifying k + 1.5 = 1.802775638 Reorder the terms: 1.5 + k = 1.802775638 Solving 1.5 + k = 1.802775638 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + k = 1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = 1.802775638 + -1.5 k = 1.802775638 + -1.5 Combine like terms: 1.802775638 + -1.5 = 0.302775638 k = 0.302775638 Simplifying k = 0.302775638

Subproblem 2

k + 1.5 = -1.802775638 Simplifying k + 1.5 = -1.802775638 Reorder the terms: 1.5 + k = -1.802775638 Solving 1.5 + k = -1.802775638 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + k = -1.802775638 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + k = -1.802775638 + -1.5 k = -1.802775638 + -1.5 Combine like terms: -1.802775638 + -1.5 = -3.302775638 k = -3.302775638 Simplifying k = -3.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. k = {0.302775638, -3.302775638}

Solution

k = {0.302775638, -3.302775638}

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