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Simplifying 10k2 = 7 + 6k Solving 10k2 = 7 + 6k Solving for variable 'k'. Reorder the terms: -7 + -6k + 10k2 = 7 + 6k + -7 + -6k Reorder the terms: -7 + -6k + 10k2 = 7 + -7 + 6k + -6k Combine like terms: 7 + -7 = 0 -7 + -6k + 10k2 = 0 + 6k + -6k -7 + -6k + 10k2 = 6k + -6k Combine like terms: 6k + -6k = 0 -7 + -6k + 10k2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -0.7 + -0.6k + k2 = 0 Move the constant term to the right: Add '0.7' to each side of the equation. -0.7 + -0.6k + 0.7 + k2 = 0 + 0.7 Reorder the terms: -0.7 + 0.7 + -0.6k + k2 = 0 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + -0.6k + k2 = 0 + 0.7 -0.6k + k2 = 0 + 0.7 Combine like terms: 0 + 0.7 = 0.7 -0.6k + k2 = 0.7 The k term is -0.6k. Take half its coefficient (-0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. -0.6k + 0.09 + k2 = 0.7 + 0.09 Reorder the terms: 0.09 + -0.6k + k2 = 0.7 + 0.09 Combine like terms: 0.7 + 0.09 = 0.79 0.09 + -0.6k + k2 = 0.79 Factor a perfect square on the left side: (k + -0.3)(k + -0.3) = 0.79 Calculate the square root of the right side: 0.888819442 Break this problem into two subproblems by setting (k + -0.3) equal to 0.888819442 and -0.888819442.Subproblem 1
k + -0.3 = 0.888819442 Simplifying k + -0.3 = 0.888819442 Reorder the terms: -0.3 + k = 0.888819442 Solving -0.3 + k = 0.888819442 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + k = 0.888819442 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + k = 0.888819442 + 0.3 k = 0.888819442 + 0.3 Combine like terms: 0.888819442 + 0.3 = 1.188819442 k = 1.188819442 Simplifying k = 1.188819442Subproblem 2
k + -0.3 = -0.888819442 Simplifying k + -0.3 = -0.888819442 Reorder the terms: -0.3 + k = -0.888819442 Solving -0.3 + k = -0.888819442 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.3' to each side of the equation. -0.3 + 0.3 + k = -0.888819442 + 0.3 Combine like terms: -0.3 + 0.3 = 0.0 0.0 + k = -0.888819442 + 0.3 k = -0.888819442 + 0.3 Combine like terms: -0.888819442 + 0.3 = -0.588819442 k = -0.588819442 Simplifying k = -0.588819442Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.188819442, -0.588819442}
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