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Simplifying 10k + 7k3 + -12k2 = 0 Reorder the terms: 10k + -12k2 + 7k3 = 0 Solving 10k + -12k2 + 7k3 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), 'k'. k(10 + -12k + 7k2) = 0Subproblem 1
Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0Subproblem 2
Set the factor '(10 + -12k + 7k2)' equal to zero and attempt to solve: Simplifying 10 + -12k + 7k2 = 0 Solving 10 + -12k + 7k2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.428571429 + -1.714285714k + k2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + -1.714285714k + -1.428571429 + k2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + -1.714285714k + k2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + -1.714285714k + k2 = 0 + -1.428571429 -1.714285714k + k2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 -1.714285714k + k2 = -1.428571429 The k term is -1.714285714k. Take half its coefficient (-0.857142857). Square it (0.7346938773) and add it to both sides. Add '0.7346938773' to each side of the equation. -1.714285714k + 0.7346938773 + k2 = -1.428571429 + 0.7346938773 Reorder the terms: 0.7346938773 + -1.714285714k + k2 = -1.428571429 + 0.7346938773 Combine like terms: -1.428571429 + 0.7346938773 = -0.6938775517 0.7346938773 + -1.714285714k + k2 = -0.6938775517 Factor a perfect square on the left side: (k + -0.857142857)(k + -0.857142857) = -0.6938775517 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
k = {0}
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