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Simplifying 10c2 + -23cd + -5d2 = 0 Reorder the terms: -23cd + 10c2 + -5d2 = 0 Solving -23cd + 10c2 + -5d2 = 0 Solving for variable 'c'. Factor a trinomial. (2c + -5d)(5c + d) = 0Subproblem 1
Set the factor '(2c + -5d)' equal to zero and attempt to solve: Simplifying 2c + -5d = 0 Solving 2c + -5d = 0 Move all terms containing c to the left, all other terms to the right. Add '5d' to each side of the equation. 2c + -5d + 5d = 0 + 5d Combine like terms: -5d + 5d = 0 2c + 0 = 0 + 5d 2c = 0 + 5d Remove the zero: 2c = 5d Divide each side by '2'. c = 2.5d Simplifying c = 2.5dSubproblem 2
Set the factor '(5c + d)' equal to zero and attempt to solve: Simplifying 5c + d = 0 Solving 5c + d = 0 Move all terms containing c to the left, all other terms to the right. Add '-1d' to each side of the equation. 5c + d + -1d = 0 + -1d Combine like terms: d + -1d = 0 5c + 0 = 0 + -1d 5c = 0 + -1d Remove the zero: 5c = -1d Divide each side by '5'. c = -0.2d Simplifying c = -0.2dSolution
c = {2.5d, -0.2d}
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