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Simplifying 4k(k + 14) = 14 Reorder the terms: 4k(14 + k) = 14 (14 * 4k + k * 4k) = 14 (56k + 4k2) = 14 Solving 56k + 4k2 = 14 Solving for variable 'k'. Reorder the terms: -14 + 56k + 4k2 = 14 + -14 Combine like terms: 14 + -14 = 0 -14 + 56k + 4k2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 28k + 2k2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 28k + 2k2)' equal to zero and attempt to solve: Simplifying -7 + 28k + 2k2 = 0 Solving -7 + 28k + 2k2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -3.5 + 14k + k2 = 0 Move the constant term to the right: Add '3.5' to each side of the equation. -3.5 + 14k + 3.5 + k2 = 0 + 3.5 Reorder the terms: -3.5 + 3.5 + 14k + k2 = 0 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + 14k + k2 = 0 + 3.5 14k + k2 = 0 + 3.5 Combine like terms: 0 + 3.5 = 3.5 14k + k2 = 3.5 The k term is 14k. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14k + 49 + k2 = 3.5 + 49 Reorder the terms: 49 + 14k + k2 = 3.5 + 49 Combine like terms: 3.5 + 49 = 52.5 49 + 14k + k2 = 52.5 Factor a perfect square on the left side: (k + 7)(k + 7) = 52.5 Calculate the square root of the right side: 7.245688373 Break this problem into two subproblems by setting (k + 7) equal to 7.245688373 and -7.245688373.Subproblem 1
k + 7 = 7.245688373 Simplifying k + 7 = 7.245688373 Reorder the terms: 7 + k = 7.245688373 Solving 7 + k = 7.245688373 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = 7.245688373 + -7 Combine like terms: 7 + -7 = 0 0 + k = 7.245688373 + -7 k = 7.245688373 + -7 Combine like terms: 7.245688373 + -7 = 0.245688373 k = 0.245688373 Simplifying k = 0.245688373Subproblem 2
k + 7 = -7.245688373 Simplifying k + 7 = -7.245688373 Reorder the terms: 7 + k = -7.245688373 Solving 7 + k = -7.245688373 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + k = -7.245688373 + -7 Combine like terms: 7 + -7 = 0 0 + k = -7.245688373 + -7 k = -7.245688373 + -7 Combine like terms: -7.245688373 + -7 = -14.245688373 k = -14.245688373 Simplifying k = -14.245688373Solution
The solution to the problem is based on the solutions from the subproblems. k = {0.245688373, -14.245688373}Solution
k = {0.245688373, -14.245688373}
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