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Simplifying 5k2 + -13k + -29 = 0 Reorder the terms: -29 + -13k + 5k2 = 0 Solving -29 + -13k + 5k2 = 0 Solving for variable 'k'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5.8 + -2.6k + k2 = 0 Move the constant term to the right: Add '5.8' to each side of the equation. -5.8 + -2.6k + 5.8 + k2 = 0 + 5.8 Reorder the terms: -5.8 + 5.8 + -2.6k + k2 = 0 + 5.8 Combine like terms: -5.8 + 5.8 = 0.0 0.0 + -2.6k + k2 = 0 + 5.8 -2.6k + k2 = 0 + 5.8 Combine like terms: 0 + 5.8 = 5.8 -2.6k + k2 = 5.8 The k term is -2.6k. Take half its coefficient (-1.3). Square it (1.69) and add it to both sides. Add '1.69' to each side of the equation. -2.6k + 1.69 + k2 = 5.8 + 1.69 Reorder the terms: 1.69 + -2.6k + k2 = 5.8 + 1.69 Combine like terms: 5.8 + 1.69 = 7.49 1.69 + -2.6k + k2 = 7.49 Factor a perfect square on the left side: (k + -1.3)(k + -1.3) = 7.49 Calculate the square root of the right side: 2.736786437 Break this problem into two subproblems by setting (k + -1.3) equal to 2.736786437 and -2.736786437.Subproblem 1
k + -1.3 = 2.736786437 Simplifying k + -1.3 = 2.736786437 Reorder the terms: -1.3 + k = 2.736786437 Solving -1.3 + k = 2.736786437 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + k = 2.736786437 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + k = 2.736786437 + 1.3 k = 2.736786437 + 1.3 Combine like terms: 2.736786437 + 1.3 = 4.036786437 k = 4.036786437 Simplifying k = 4.036786437Subproblem 2
k + -1.3 = -2.736786437 Simplifying k + -1.3 = -2.736786437 Reorder the terms: -1.3 + k = -2.736786437 Solving -1.3 + k = -2.736786437 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '1.3' to each side of the equation. -1.3 + 1.3 + k = -2.736786437 + 1.3 Combine like terms: -1.3 + 1.3 = 0.0 0.0 + k = -2.736786437 + 1.3 k = -2.736786437 + 1.3 Combine like terms: -2.736786437 + 1.3 = -1.436786437 k = -1.436786437 Simplifying k = -1.436786437Solution
The solution to the problem is based on the solutions from the subproblems. k = {4.036786437, -1.436786437}
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