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Simplifying 4k2 + -28k = 49 Reorder the terms: -28k + 4k2 = 49 Solving -28k + 4k2 = 49 Solving for variable 'k'. Reorder the terms: -49 + -28k + 4k2 = 49 + -49 Combine like terms: 49 + -49 = 0 -49 + -28k + 4k2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -12.25 + -7k + k2 = 0 Move the constant term to the right: Add '12.25' to each side of the equation. -12.25 + -7k + 12.25 + k2 = 0 + 12.25 Reorder the terms: -12.25 + 12.25 + -7k + k2 = 0 + 12.25 Combine like terms: -12.25 + 12.25 = 0.00 0.00 + -7k + k2 = 0 + 12.25 -7k + k2 = 0 + 12.25 Combine like terms: 0 + 12.25 = 12.25 -7k + k2 = 12.25 The k term is -7k. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7k + 12.25 + k2 = 12.25 + 12.25 Reorder the terms: 12.25 + -7k + k2 = 12.25 + 12.25 Combine like terms: 12.25 + 12.25 = 24.5 12.25 + -7k + k2 = 24.5 Factor a perfect square on the left side: (k + -3.5)(k + -3.5) = 24.5 Calculate the square root of the right side: 4.949747468 Break this problem into two subproblems by setting (k + -3.5) equal to 4.949747468 and -4.949747468.Subproblem 1
k + -3.5 = 4.949747468 Simplifying k + -3.5 = 4.949747468 Reorder the terms: -3.5 + k = 4.949747468 Solving -3.5 + k = 4.949747468 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = 4.949747468 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = 4.949747468 + 3.5 k = 4.949747468 + 3.5 Combine like terms: 4.949747468 + 3.5 = 8.449747468 k = 8.449747468 Simplifying k = 8.449747468Subproblem 2
k + -3.5 = -4.949747468 Simplifying k + -3.5 = -4.949747468 Reorder the terms: -3.5 + k = -4.949747468 Solving -3.5 + k = -4.949747468 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + k = -4.949747468 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = -4.949747468 + 3.5 k = -4.949747468 + 3.5 Combine like terms: -4.949747468 + 3.5 = -1.449747468 k = -1.449747468 Simplifying k = -1.449747468Solution
The solution to the problem is based on the solutions from the subproblems. k = {8.449747468, -1.449747468}
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