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Simplifying -12k2 + 20k + 39 = 0 Reorder the terms: 39 + 20k + -12k2 = 0 Solving 39 + 20k + -12k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. -3.25 + -1.666666667k + k2 = 0 Move the constant term to the right: Add '3.25' to each side of the equation. -3.25 + -1.666666667k + 3.25 + k2 = 0 + 3.25 Reorder the terms: -3.25 + 3.25 + -1.666666667k + k2 = 0 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + -1.666666667k + k2 = 0 + 3.25 -1.666666667k + k2 = 0 + 3.25 Combine like terms: 0 + 3.25 = 3.25 -1.666666667k + k2 = 3.25 The k term is -1.666666667k. Take half its coefficient (-0.8333333335). Square it (0.6944444447) and add it to both sides. Add '0.6944444447' to each side of the equation. -1.666666667k + 0.6944444447 + k2 = 3.25 + 0.6944444447 Reorder the terms: 0.6944444447 + -1.666666667k + k2 = 3.25 + 0.6944444447 Combine like terms: 3.25 + 0.6944444447 = 3.9444444447 0.6944444447 + -1.666666667k + k2 = 3.9444444447 Factor a perfect square on the left side: (k + -0.8333333335)(k + -0.8333333335) = 3.9444444447 Calculate the square root of the right side: 1.986062548 Break this problem into two subproblems by setting (k + -0.8333333335) equal to 1.986062548 and -1.986062548.Subproblem 1
k + -0.8333333335 = 1.986062548 Simplifying k + -0.8333333335 = 1.986062548 Reorder the terms: -0.8333333335 + k = 1.986062548 Solving -0.8333333335 + k = 1.986062548 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + k = 1.986062548 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + k = 1.986062548 + 0.8333333335 k = 1.986062548 + 0.8333333335 Combine like terms: 1.986062548 + 0.8333333335 = 2.8193958815 k = 2.8193958815 Simplifying k = 2.8193958815Subproblem 2
k + -0.8333333335 = -1.986062548 Simplifying k + -0.8333333335 = -1.986062548 Reorder the terms: -0.8333333335 + k = -1.986062548 Solving -0.8333333335 + k = -1.986062548 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.8333333335' to each side of the equation. -0.8333333335 + 0.8333333335 + k = -1.986062548 + 0.8333333335 Combine like terms: -0.8333333335 + 0.8333333335 = 0.0000000000 0.0000000000 + k = -1.986062548 + 0.8333333335 k = -1.986062548 + 0.8333333335 Combine like terms: -1.986062548 + 0.8333333335 = -1.1527292145 k = -1.1527292145 Simplifying k = -1.1527292145Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.8193958815, -1.1527292145}
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