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Simplifying 2x2 + 5kx + -3k2 = 0 Reorder the terms: 5kx + -3k2 + 2x2 = 0 Solving 5kx + -3k2 + 2x2 = 0 Solving for variable 'k'. Factor a trinomial. (-3k + -1x)(k + -2x) = 0Subproblem 1
Set the factor '(-3k + -1x)' equal to zero and attempt to solve: Simplifying -3k + -1x = 0 Solving -3k + -1x = 0 Move all terms containing k to the left, all other terms to the right. Add 'x' to each side of the equation. -3k + -1x + x = 0 + x Combine like terms: -1x + x = 0 -3k + 0 = 0 + x -3k = 0 + x Remove the zero: -3k = x Divide each side by '-3'. k = -0.3333333333x Simplifying k = -0.3333333333xSubproblem 2
Set the factor '(k + -2x)' equal to zero and attempt to solve: Simplifying k + -2x = 0 Solving k + -2x = 0 Move all terms containing k to the left, all other terms to the right. Add '2x' to each side of the equation. k + -2x + 2x = 0 + 2x Combine like terms: -2x + 2x = 0 k + 0 = 0 + 2x k = 0 + 2x Remove the zero: k = 2x Simplifying k = 2xSolution
k = {-0.3333333333x, 2x}
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