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Simplifying 378k2 + 216k + 70 = 0 Reorder the terms: 70 + 216k + 378k2 = 0 Solving 70 + 216k + 378k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '2'. 2(35 + 108k + 189k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(35 + 108k + 189k2)' equal to zero and attempt to solve: Simplifying 35 + 108k + 189k2 = 0 Solving 35 + 108k + 189k2 = 0 Begin completing the square. Divide all terms by 189 the coefficient of the squared term: Divide each side by '189'. 0.1851851852 + 0.5714285714k + k2 = 0 Move the constant term to the right: Add '-0.1851851852' to each side of the equation. 0.1851851852 + 0.5714285714k + -0.1851851852 + k2 = 0 + -0.1851851852 Reorder the terms: 0.1851851852 + -0.1851851852 + 0.5714285714k + k2 = 0 + -0.1851851852 Combine like terms: 0.1851851852 + -0.1851851852 = 0.0000000000 0.0000000000 + 0.5714285714k + k2 = 0 + -0.1851851852 0.5714285714k + k2 = 0 + -0.1851851852 Combine like terms: 0 + -0.1851851852 = -0.1851851852 0.5714285714k + k2 = -0.1851851852 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 = -0.1851851852 + 0.08163265305 Reorder the terms: 0.08163265305 + 0.5714285714k + k2 = -0.1851851852 + 0.08163265305 Combine like terms: -0.1851851852 + 0.08163265305 = -0.10355253215 0.08163265305 + 0.5714285714k + k2 = -0.10355253215 Factor a perfect square on the left side: (k + 0.2857142857)(k + 0.2857142857) = -0.10355253215 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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