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Simplifying 10k2 = 7k + 18 Reorder the terms: 10k2 = 18 + 7k Solving 10k2 = 18 + 7k Solving for variable 'k'. Reorder the terms: -18 + -7k + 10k2 = 18 + 7k + -18 + -7k Reorder the terms: -18 + -7k + 10k2 = 18 + -18 + 7k + -7k Combine like terms: 18 + -18 = 0 -18 + -7k + 10k2 = 0 + 7k + -7k -18 + -7k + 10k2 = 7k + -7k Combine like terms: 7k + -7k = 0 -18 + -7k + 10k2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -1.8 + -0.7k + k2 = 0 Move the constant term to the right: Add '1.8' to each side of the equation. -1.8 + -0.7k + 1.8 + k2 = 0 + 1.8 Reorder the terms: -1.8 + 1.8 + -0.7k + k2 = 0 + 1.8 Combine like terms: -1.8 + 1.8 = 0.0 0.0 + -0.7k + k2 = 0 + 1.8 -0.7k + k2 = 0 + 1.8 Combine like terms: 0 + 1.8 = 1.8 -0.7k + k2 = 1.8 The k term is -0.7k. Take half its coefficient (-0.35). Square it (0.1225) and add it to both sides. Add '0.1225' to each side of the equation. -0.7k + 0.1225 + k2 = 1.8 + 0.1225 Reorder the terms: 0.1225 + -0.7k + k2 = 1.8 + 0.1225 Combine like terms: 1.8 + 0.1225 = 1.9225 0.1225 + -0.7k + k2 = 1.9225 Factor a perfect square on the left side: (k + -0.35)(k + -0.35) = 1.9225 Calculate the square root of the right side: 1.386542462 Break this problem into two subproblems by setting (k + -0.35) equal to 1.386542462 and -1.386542462.Subproblem 1
k + -0.35 = 1.386542462 Simplifying k + -0.35 = 1.386542462 Reorder the terms: -0.35 + k = 1.386542462 Solving -0.35 + k = 1.386542462 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + k = 1.386542462 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + k = 1.386542462 + 0.35 k = 1.386542462 + 0.35 Combine like terms: 1.386542462 + 0.35 = 1.736542462 k = 1.736542462 Simplifying k = 1.736542462Subproblem 2
k + -0.35 = -1.386542462 Simplifying k + -0.35 = -1.386542462 Reorder the terms: -0.35 + k = -1.386542462 Solving -0.35 + k = -1.386542462 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '0.35' to each side of the equation. -0.35 + 0.35 + k = -1.386542462 + 0.35 Combine like terms: -0.35 + 0.35 = 0.00 0.00 + k = -1.386542462 + 0.35 k = -1.386542462 + 0.35 Combine like terms: -1.386542462 + 0.35 = -1.036542462 k = -1.036542462 Simplifying k = -1.036542462Solution
The solution to the problem is based on the solutions from the subproblems. k = {1.736542462, -1.036542462}
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