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Simplifying 5(3 + -2k) * 8(3k + -4) + -4(1 + 7k) = 0 Reorder the terms: 5(3 + -2k) * 8(-4 + 3k) + -4(1 + 7k) = 0 Reorder the terms for easier multiplication: 5 * 8(3 + -2k)(-4 + 3k) + -4(1 + 7k) = 0 Multiply 5 * 8 40(3 + -2k)(-4 + 3k) + -4(1 + 7k) = 0 Multiply (3 + -2k) * (-4 + 3k) 40(3(-4 + 3k) + -2k * (-4 + 3k)) + -4(1 + 7k) = 0 40((-4 * 3 + 3k * 3) + -2k * (-4 + 3k)) + -4(1 + 7k) = 0 40((-12 + 9k) + -2k * (-4 + 3k)) + -4(1 + 7k) = 0 40(-12 + 9k + (-4 * -2k + 3k * -2k)) + -4(1 + 7k) = 0 40(-12 + 9k + (8k + -6k2)) + -4(1 + 7k) = 0 Combine like terms: 9k + 8k = 17k 40(-12 + 17k + -6k2) + -4(1 + 7k) = 0 (-12 * 40 + 17k * 40 + -6k2 * 40) + -4(1 + 7k) = 0 (-480 + 680k + -240k2) + -4(1 + 7k) = 0 -480 + 680k + -240k2 + (1 * -4 + 7k * -4) = 0 -480 + 680k + -240k2 + (-4 + -28k) = 0 Reorder the terms: -480 + -4 + 680k + -28k + -240k2 = 0 Combine like terms: -480 + -4 = -484 -484 + 680k + -28k + -240k2 = 0 Combine like terms: 680k + -28k = 652k -484 + 652k + -240k2 = 0 Solving -484 + 652k + -240k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '4'. 4(-121 + 163k + -60k2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-121 + 163k + -60k2)' equal to zero and attempt to solve: Simplifying -121 + 163k + -60k2 = 0 Solving -121 + 163k + -60k2 = 0 Begin completing the square. Divide all terms by -60 the coefficient of the squared term: Divide each side by '-60'. 2.016666667 + -2.716666667k + k2 = 0.0 Move the constant term to the right: Add '-2.016666667' to each side of the equation. 2.016666667 + -2.716666667k + -2.016666667 + k2 = 0.0 + -2.016666667 Reorder the terms: 2.016666667 + -2.016666667 + -2.716666667k + k2 = 0.0 + -2.016666667 Combine like terms: 2.016666667 + -2.016666667 = 0.000000000 0.000000000 + -2.716666667k + k2 = 0.0 + -2.016666667 -2.716666667k + k2 = 0.0 + -2.016666667 Combine like terms: 0.0 + -2.016666667 = -2.016666667 -2.716666667k + k2 = -2.016666667 The k term is -2.716666667k. Take half its coefficient (-1.358333334). Square it (1.845069446) and add it to both sides. Add '1.845069446' to each side of the equation. -2.716666667k + 1.845069446 + k2 = -2.016666667 + 1.845069446 Reorder the terms: 1.845069446 + -2.716666667k + k2 = -2.016666667 + 1.845069446 Combine like terms: -2.016666667 + 1.845069446 = -0.171597221 1.845069446 + -2.716666667k + k2 = -0.171597221 Factor a perfect square on the left side: (k + -1.358333334)(k + -1.358333334) = -0.171597221 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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