18(k^2-12k-6)=

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Solution for 18(k^2-12k-6)= equation:


Simplifying
18(k2 + -12k + -6) = 0

Reorder the terms:
18(-6 + -12k + k2) = 0
(-6 * 18 + -12k * 18 + k2 * 18) = 0
(-108 + -216k + 18k2) = 0

Solving
-108 + -216k + 18k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '18'.
18(-6 + -12k + k2) = 0

Ignore the factor 18.

Subproblem 1

Set the factor '(-6 + -12k + k2)' equal to zero and attempt to solve: Simplifying -6 + -12k + k2 = 0 Solving -6 + -12k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '6' to each side of the equation. -6 + -12k + 6 + k2 = 0 + 6 Reorder the terms: -6 + 6 + -12k + k2 = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -12k + k2 = 0 + 6 -12k + k2 = 0 + 6 Combine like terms: 0 + 6 = 6 -12k + k2 = 6 The k term is -12k. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12k + 36 + k2 = 6 + 36 Reorder the terms: 36 + -12k + k2 = 6 + 36 Combine like terms: 6 + 36 = 42 36 + -12k + k2 = 42 Factor a perfect square on the left side: (k + -6)(k + -6) = 42 Calculate the square root of the right side: 6.480740698 Break this problem into two subproblems by setting (k + -6) equal to 6.480740698 and -6.480740698.

Subproblem 1

k + -6 = 6.480740698 Simplifying k + -6 = 6.480740698 Reorder the terms: -6 + k = 6.480740698 Solving -6 + k = 6.480740698 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = 6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + k = 6.480740698 + 6 k = 6.480740698 + 6 Combine like terms: 6.480740698 + 6 = 12.480740698 k = 12.480740698 Simplifying k = 12.480740698

Subproblem 2

k + -6 = -6.480740698 Simplifying k + -6 = -6.480740698 Reorder the terms: -6 + k = -6.480740698 Solving -6 + k = -6.480740698 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + k = -6.480740698 + 6 Combine like terms: -6 + 6 = 0 0 + k = -6.480740698 + 6 k = -6.480740698 + 6 Combine like terms: -6.480740698 + 6 = -0.480740698 k = -0.480740698 Simplifying k = -0.480740698

Solution

The solution to the problem is based on the solutions from the subproblems. k = {12.480740698, -0.480740698}

Solution

k = {12.480740698, -0.480740698}

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