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Simplifying 3k2 + 12k + -79 = 7 Reorder the terms: -79 + 12k + 3k2 = 7 Solving -79 + 12k + 3k2 = 7 Solving for variable 'k'. Reorder the terms: -79 + -7 + 12k + 3k2 = 7 + -7 Combine like terms: -79 + -7 = -86 -86 + 12k + 3k2 = 7 + -7 Combine like terms: 7 + -7 = 0 -86 + 12k + 3k2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -28.66666667 + 4k + k2 = 0 Move the constant term to the right: Add '28.66666667' to each side of the equation. -28.66666667 + 4k + 28.66666667 + k2 = 0 + 28.66666667 Reorder the terms: -28.66666667 + 28.66666667 + 4k + k2 = 0 + 28.66666667 Combine like terms: -28.66666667 + 28.66666667 = 0.00000000 0.00000000 + 4k + k2 = 0 + 28.66666667 4k + k2 = 0 + 28.66666667 Combine like terms: 0 + 28.66666667 = 28.66666667 4k + k2 = 28.66666667 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = 28.66666667 + 4 Reorder the terms: 4 + 4k + k2 = 28.66666667 + 4 Combine like terms: 28.66666667 + 4 = 32.66666667 4 + 4k + k2 = 32.66666667 Factor a perfect square on the left side: (k + 2)(k + 2) = 32.66666667 Calculate the square root of the right side: 5.715476067 Break this problem into two subproblems by setting (k + 2) equal to 5.715476067 and -5.715476067.Subproblem 1
k + 2 = 5.715476067 Simplifying k + 2 = 5.715476067 Reorder the terms: 2 + k = 5.715476067 Solving 2 + k = 5.715476067 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 5.715476067 + -2 Combine like terms: 2 + -2 = 0 0 + k = 5.715476067 + -2 k = 5.715476067 + -2 Combine like terms: 5.715476067 + -2 = 3.715476067 k = 3.715476067 Simplifying k = 3.715476067Subproblem 2
k + 2 = -5.715476067 Simplifying k + 2 = -5.715476067 Reorder the terms: 2 + k = -5.715476067 Solving 2 + k = -5.715476067 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = -5.715476067 + -2 Combine like terms: 2 + -2 = 0 0 + k = -5.715476067 + -2 k = -5.715476067 + -2 Combine like terms: -5.715476067 + -2 = -7.715476067 k = -7.715476067 Simplifying k = -7.715476067Solution
The solution to the problem is based on the solutions from the subproblems. k = {3.715476067, -7.715476067}
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