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Simplifying 7(-2 + -1k) + -1k(1 + 3k) = 0 (-2 * 7 + -1k * 7) + -1k(1 + 3k) = 0 (-14 + -7k) + -1k(1 + 3k) = 0 -14 + -7k + (1 * -1k + 3k * -1k) = 0 -14 + -7k + (-1k + -3k2) = 0 Combine like terms: -7k + -1k = -8k -14 + -8k + -3k2 = 0 Solving -14 + -8k + -3k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-1'. -1(14 + 8k + 3k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(14 + 8k + 3k2)' equal to zero and attempt to solve: Simplifying 14 + 8k + 3k2 = 0 Solving 14 + 8k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 4.666666667 + 2.666666667k + k2 = 0 Move the constant term to the right: Add '-4.666666667' to each side of the equation. 4.666666667 + 2.666666667k + -4.666666667 + k2 = 0 + -4.666666667 Reorder the terms: 4.666666667 + -4.666666667 + 2.666666667k + k2 = 0 + -4.666666667 Combine like terms: 4.666666667 + -4.666666667 = 0.000000000 0.000000000 + 2.666666667k + k2 = 0 + -4.666666667 2.666666667k + k2 = 0 + -4.666666667 Combine like terms: 0 + -4.666666667 = -4.666666667 2.666666667k + k2 = -4.666666667 The k term is 2.666666667k. Take half its coefficient (1.333333334). Square it (1.777777780) and add it to both sides. Add '1.777777780' to each side of the equation. 2.666666667k + 1.777777780 + k2 = -4.666666667 + 1.777777780 Reorder the terms: 1.777777780 + 2.666666667k + k2 = -4.666666667 + 1.777777780 Combine like terms: -4.666666667 + 1.777777780 = -2.888888887 1.777777780 + 2.666666667k + k2 = -2.888888887 Factor a perfect square on the left side: (k + 1.333333334)(k + 1.333333334) = -2.888888887 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. The solution to this equation could not be determined.
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