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Simplifying 4k2 + -28k = -9 Reorder the terms: -28k + 4k2 = -9 Solving -28k + 4k2 = -9 Solving for variable 'k'. Reorder the terms: 9 + -28k + 4k2 = -9 + 9 Combine like terms: -9 + 9 = 0 9 + -28k + 4k2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 2.25 + -7k + k2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -7k + -2.25 + k2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -7k + k2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -7k + k2 = 0 + -2.25 -7k + k2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -7k + k2 = -2.25 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 = -2.25 + 12.25 Reorder the terms: 12.25 + -7k + k2 = -2.25 + 12.25 Combine like terms: -2.25 + 12.25 = 10 12.25 + -7k + k2 = 10 Factor a perfect square on the left side: (k + -3.5)(k + -3.5) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (k + -3.5) equal to 3.16227766 and -3.16227766.Subproblem 1
k + -3.5 = 3.16227766 Simplifying k + -3.5 = 3.16227766 Reorder the terms: -3.5 + k = 3.16227766 Solving -3.5 + k = 3.16227766 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 = 3.16227766 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = 3.16227766 + 3.5 k = 3.16227766 + 3.5 Combine like terms: 3.16227766 + 3.5 = 6.66227766 k = 6.66227766 Simplifying k = 6.66227766Subproblem 2
k + -3.5 = -3.16227766 Simplifying k + -3.5 = -3.16227766 Reorder the terms: -3.5 + k = -3.16227766 Solving -3.5 + k = -3.16227766 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 = -3.16227766 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + k = -3.16227766 + 3.5 k = -3.16227766 + 3.5 Combine like terms: -3.16227766 + 3.5 = 0.33772234 k = 0.33772234 Simplifying k = 0.33772234Solution
The solution to the problem is based on the solutions from the subproblems. k = {6.66227766, 0.33772234}
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