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Simplifying -2k(-7k + 4) + 9 = -13 Reorder the terms: -2k(4 + -7k) + 9 = -13 (4 * -2k + -7k * -2k) + 9 = -13 (-8k + 14k2) + 9 = -13 Reorder the terms: 9 + -8k + 14k2 = -13 Solving 9 + -8k + 14k2 = -13 Solving for variable 'k'. Reorder the terms: 9 + 13 + -8k + 14k2 = -13 + 13 Combine like terms: 9 + 13 = 22 22 + -8k + 14k2 = -13 + 13 Combine like terms: -13 + 13 = 0 22 + -8k + 14k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(11 + -4k + 7k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(11 + -4k + 7k2)' equal to zero and attempt to solve: Simplifying 11 + -4k + 7k2 = 0 Solving 11 + -4k + 7k2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.571428571 + -0.5714285714k + k2 = 0 Move the constant term to the right: Add '-1.571428571' to each side of the equation. 1.571428571 + -0.5714285714k + -1.571428571 + k2 = 0 + -1.571428571 Reorder the terms: 1.571428571 + -1.571428571 + -0.5714285714k + k2 = 0 + -1.571428571 Combine like terms: 1.571428571 + -1.571428571 = 0.000000000 0.000000000 + -0.5714285714k + k2 = 0 + -1.571428571 -0.5714285714k + k2 = 0 + -1.571428571 Combine like terms: 0 + -1.571428571 = -1.571428571 -0.5714285714k + k2 = -1.571428571 The k term is -0.5714285714k. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714k + 0.08163265305 + k2 = -1.571428571 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714k + k2 = -1.571428571 + 0.08163265305 Combine like terms: -1.571428571 + 0.08163265305 = -1.48979591795 0.08163265305 + -0.5714285714k + k2 = -1.48979591795 Factor a perfect square on the left side: (k + -0.2857142857)(k + -0.2857142857) = -1.48979591795 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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