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Simplifying 25k2 + -22k + 7 = 4 Reorder the terms: 7 + -22k + 25k2 = 4 Solving 7 + -22k + 25k2 = 4 Solving for variable 'k'. Reorder the terms: 7 + -4 + -22k + 25k2 = 4 + -4 Combine like terms: 7 + -4 = 3 3 + -22k + 25k2 = 4 + -4 Combine like terms: 4 + -4 = 0 3 + -22k + 25k2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.12 + -0.88k + k2 = 0 Move the constant term to the right: Add '-0.12' to each side of the equation. 0.12 + -0.88k + -0.12 + k2 = 0 + -0.12 Reorder the terms: 0.12 + -0.12 + -0.88k + k2 = 0 + -0.12 Combine like terms: 0.12 + -0.12 = 0.00 0.00 + -0.88k + k2 = 0 + -0.12 -0.88k + k2 = 0 + -0.12 Combine like terms: 0 + -0.12 = -0.12 -0.88k + k2 = -0.12 The k term is -0.88k. Take half its coefficient (-0.44). Square it (0.1936) and add it to both sides. Add '0.1936' to each side of the equation. -0.88k + 0.1936 + k2 = -0.12 + 0.1936 Reorder the terms: 0.1936 + -0.88k + k2 = -0.12 + 0.1936 Combine like terms: -0.12 + 0.1936 = 0.0736 0.1936 + -0.88k + k2 = 0.0736 Factor a perfect square on the left side: (k + -0.44)(k + -0.44) = 0.0736 Calculate the square root of the right side: 0.271293199 Break this problem into two subproblems by setting (k + -0.44) equal to 0.271293199 and -0.271293199.Subproblem 1
k + -0.44 = 0.271293199 Simplifying k + -0.44 = 0.271293199 Reorder the terms: -0.44 + k = 0.271293199 Solving -0.44 + k = 0.271293199 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.44' to each side of the equation. -0.44 + 0.44 + k = 0.271293199 + 0.44 Combine like terms: -0.44 + 0.44 = 0.00 0.00 + k = 0.271293199 + 0.44 k = 0.271293199 + 0.44 Combine like terms: 0.271293199 + 0.44 = 0.711293199 k = 0.711293199 Simplifying k = 0.711293199Subproblem 2
k + -0.44 = -0.271293199 Simplifying k + -0.44 = -0.271293199 Reorder the terms: -0.44 + k = -0.271293199 Solving -0.44 + k = -0.271293199 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.44' to each side of the equation. -0.44 + 0.44 + k = -0.271293199 + 0.44 Combine like terms: -0.44 + 0.44 = 0.00 0.00 + k = -0.271293199 + 0.44 k = -0.271293199 + 0.44 Combine like terms: -0.271293199 + 0.44 = 0.168706801 k = 0.168706801 Simplifying k = 0.168706801Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.711293199, 0.168706801}
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