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Simplifying 2k2 + -14k + 30 = 2 Reorder the terms: 30 + -14k + 2k2 = 2 Solving 30 + -14k + 2k2 = 2 Solving for variable 'k'. Reorder the terms: 30 + -2 + -14k + 2k2 = 2 + -2 Combine like terms: 30 + -2 = 28 28 + -14k + 2k2 = 2 + -2 Combine like terms: 2 + -2 = 0 28 + -14k + 2k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -7k + k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(14 + -7k + k2)' equal to zero and attempt to solve: Simplifying 14 + -7k + k2 = 0 Solving 14 + -7k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -7k + -14 + k2 = 0 + -14 Reorder the terms: 14 + -14 + -7k + k2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -7k + k2 = 0 + -14 -7k + k2 = 0 + -14 Combine like terms: 0 + -14 = -14 -7k + k2 = -14 The k term is -7k. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7k + 12.25 + k2 = -14 + 12.25 Reorder the terms: 12.25 + -7k + k2 = -14 + 12.25 Combine like terms: -14 + 12.25 = -1.75 12.25 + -7k + k2 = -1.75 Factor a perfect square on the left side: (k + -3.5)(k + -3.5) = -1.75 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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