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Simplifying -7k2 = 4k + 10 Reorder the terms: -7k2 = 10 + 4k Solving -7k2 = 10 + 4k Solving for variable 'k'. Reorder the terms: -10 + -4k + -7k2 = 10 + 4k + -10 + -4k Reorder the terms: -10 + -4k + -7k2 = 10 + -10 + 4k + -4k Combine like terms: 10 + -10 = 0 -10 + -4k + -7k2 = 0 + 4k + -4k -10 + -4k + -7k2 = 4k + -4k Combine like terms: 4k + -4k = 0 -10 + -4k + -7k2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(10 + 4k + 7k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(10 + 4k + 7k2)' equal to zero and attempt to solve: Simplifying 10 + 4k + 7k2 = 0 Solving 10 + 4k + 7k2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 1.428571429 + 0.5714285714k + k2 = 0 Move the constant term to the right: Add '-1.428571429' to each side of the equation. 1.428571429 + 0.5714285714k + -1.428571429 + k2 = 0 + -1.428571429 Reorder the terms: 1.428571429 + -1.428571429 + 0.5714285714k + k2 = 0 + -1.428571429 Combine like terms: 1.428571429 + -1.428571429 = 0.000000000 0.000000000 + 0.5714285714k + k2 = 0 + -1.428571429 0.5714285714k + k2 = 0 + -1.428571429 Combine like terms: 0 + -1.428571429 = -1.428571429 0.5714285714k + k2 = -1.428571429 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 = -1.428571429 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714k + k2 = -1.428571429 + 0.08163265305 Combine like terms: -1.428571429 + 0.08163265305 = -1.34693877595 0.08163265305 + 0.5714285714k + k2 = -1.34693877595 Factor a perfect square on the left side: (k + 0.2857142857)(k + 0.2857142857) = -1.34693877595 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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