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Simplifying -5 + -1(30k2 + 12k) = 0 Reorder the terms: -5 + -1(12k + 30k2) = 0 -5 + (12k * -1 + 30k2 * -1) = 0 -5 + (-12k + -30k2) = 0 Solving -5 + -12k + -30k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '-1'. -1(5 + 12k + 30k2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(5 + 12k + 30k2)' equal to zero and attempt to solve: Simplifying 5 + 12k + 30k2 = 0 Solving 5 + 12k + 30k2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. 0.1666666667 + 0.4k + k2 = 0.0 Move the constant term to the right: Add '-0.1666666667' to each side of the equation. 0.1666666667 + 0.4k + -0.1666666667 + k2 = 0.0 + -0.1666666667 Reorder the terms: 0.1666666667 + -0.1666666667 + 0.4k + k2 = 0.0 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + 0.4k + k2 = 0.0 + -0.1666666667 0.4k + k2 = 0.0 + -0.1666666667 Combine like terms: 0.0 + -0.1666666667 = -0.1666666667 0.4k + k2 = -0.1666666667 The k term is 0.4k. Take half its coefficient (0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. 0.4k + 0.04 + k2 = -0.1666666667 + 0.04 Reorder the terms: 0.04 + 0.4k + k2 = -0.1666666667 + 0.04 Combine like terms: -0.1666666667 + 0.04 = -0.1266666667 0.04 + 0.4k + k2 = -0.1266666667 Factor a perfect square on the left side: (k + 0.2)(k + 0.2) = -0.1266666667 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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