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Simplifying 5k2 + 20k + -100 = 0 Reorder the terms: -100 + 20k + 5k2 = 0 Solving -100 + 20k + 5k2 = 0 Solving for variable 'k'. Factor out the Greatest Common Factor (GCF), '5'. 5(-20 + 4k + k2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-20 + 4k + k2)' equal to zero and attempt to solve: Simplifying -20 + 4k + k2 = 0 Solving -20 + 4k + k2 = 0 Begin completing the square. Move the constant term to the right: Add '20' to each side of the equation. -20 + 4k + 20 + k2 = 0 + 20 Reorder the terms: -20 + 20 + 4k + k2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 4k + k2 = 0 + 20 4k + k2 = 0 + 20 Combine like terms: 0 + 20 = 20 4k + k2 = 20 The k term is 4k. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4k + 4 + k2 = 20 + 4 Reorder the terms: 4 + 4k + k2 = 20 + 4 Combine like terms: 20 + 4 = 24 4 + 4k + k2 = 24 Factor a perfect square on the left side: (k + 2)(k + 2) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (k + 2) equal to 4.898979486 and -4.898979486.Subproblem 1
k + 2 = 4.898979486 Simplifying k + 2 = 4.898979486 Reorder the terms: 2 + k = 4.898979486 Solving 2 + k = 4.898979486 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + k = 4.898979486 + -2 k = 4.898979486 + -2 Combine like terms: 4.898979486 + -2 = 2.898979486 k = 2.898979486 Simplifying k = 2.898979486Subproblem 2
k + 2 = -4.898979486 Simplifying k + 2 = -4.898979486 Reorder the terms: 2 + k = -4.898979486 Solving 2 + k = -4.898979486 Solving for variable 'k'. Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = -4.898979486 + -2 Combine like terms: 2 + -2 = 0 0 + k = -4.898979486 + -2 k = -4.898979486 + -2 Combine like terms: -4.898979486 + -2 = -6.898979486 k = -6.898979486 Simplifying k = -6.898979486Solution
The solution to the problem is based on the solutions from the subproblems. k = {2.898979486, -6.898979486}Solution
k = {2.898979486, -6.898979486}
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