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Simplifying x2 + -5kx + -50k2 = 0 Reorder the terms: -5kx + -50k2 + x2 = 0 Solving -5kx + -50k2 + x2 = 0 Solving for variable 'k'. Factor a trinomial. (-5k + -1x)(10k + -1x) = 0Subproblem 1
Set the factor '(-5k + -1x)' equal to zero and attempt to solve: Simplifying -5k + -1x = 0 Solving -5k + -1x = 0 Move all terms containing k to the left, all other terms to the right. Add 'x' to each side of the equation. -5k + -1x + x = 0 + x Combine like terms: -1x + x = 0 -5k + 0 = 0 + x -5k = 0 + x Remove the zero: -5k = x Divide each side by '-5'. k = -0.2x Simplifying k = -0.2xSubproblem 2
Set the factor '(10k + -1x)' equal to zero and attempt to solve: Simplifying 10k + -1x = 0 Solving 10k + -1x = 0 Move all terms containing k to the left, all other terms to the right. Add 'x' to each side of the equation. 10k + -1x + x = 0 + x Combine like terms: -1x + x = 0 10k + 0 = 0 + x 10k = 0 + x Remove the zero: 10k = x Divide each side by '10'. k = 0.1x Simplifying k = 0.1xSolution
k = {-0.2x, 0.1x}
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