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Simplifying -7k(4k + -5) + -8 = 223 Reorder the terms: -7k(-5 + 4k) + -8 = 223 (-5 * -7k + 4k * -7k) + -8 = 223 (35k + -28k2) + -8 = 223 Reorder the terms: -8 + 35k + -28k2 = 223 Solving -8 + 35k + -28k2 = 223 Solving for variable 'k'. Reorder the terms: -8 + -223 + 35k + -28k2 = 223 + -223 Combine like terms: -8 + -223 = -231 -231 + 35k + -28k2 = 223 + -223 Combine like terms: 223 + -223 = 0 -231 + 35k + -28k2 = 0 Factor out the Greatest Common Factor (GCF), '7'. 7(-33 + 5k + -4k2) = 0 Ignore the factor 7.Subproblem 1
Set the factor '(-33 + 5k + -4k2)' equal to zero and attempt to solve: Simplifying -33 + 5k + -4k2 = 0 Solving -33 + 5k + -4k2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 8.25 + -1.25k + k2 = 0 Move the constant term to the right: Add '-8.25' to each side of the equation. 8.25 + -1.25k + -8.25 + k2 = 0 + -8.25 Reorder the terms: 8.25 + -8.25 + -1.25k + k2 = 0 + -8.25 Combine like terms: 8.25 + -8.25 = 0.00 0.00 + -1.25k + k2 = 0 + -8.25 -1.25k + k2 = 0 + -8.25 Combine like terms: 0 + -8.25 = -8.25 -1.25k + k2 = -8.25 The k term is -1.25k. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25k + 0.390625 + k2 = -8.25 + 0.390625 Reorder the terms: 0.390625 + -1.25k + k2 = -8.25 + 0.390625 Combine like terms: -8.25 + 0.390625 = -7.859375 0.390625 + -1.25k + k2 = -7.859375 Factor a perfect square on the left side: (k + -0.625)(k + -0.625) = -7.859375 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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