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Simplifying V(x) = -5x2 + 50x Multiply V * x xV = -5x2 + 50x Reorder the terms: xV = 50x + -5x2 Solving xV = 50x + -5x2 Solving for variable 'x'. Reorder the terms: -50x + xV + 5x2 = 50x + -5x2 + -50x + 5x2 Reorder the terms: -50x + xV + 5x2 = 50x + -50x + -5x2 + 5x2 Combine like terms: 50x + -50x = 0 -50x + xV + 5x2 = 0 + -5x2 + 5x2 -50x + xV + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -50x + xV + 5x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-50 + V + 5x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-50 + V + 5x)' equal to zero and attempt to solve: Simplifying -50 + V + 5x = 0 Solving -50 + V + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + V + 50 + 5x = 0 + 50 Reorder the terms: -50 + 50 + V + 5x = 0 + 50 Combine like terms: -50 + 50 = 0 0 + V + 5x = 0 + 50 V + 5x = 0 + 50 Combine like terms: 0 + 50 = 50 V + 5x = 50 Add '-1V' to each side of the equation. V + -1V + 5x = 50 + -1V Combine like terms: V + -1V = 0 0 + 5x = 50 + -1V 5x = 50 + -1V Divide each side by '5'. x = 10 + -0.2V Simplifying x = 10 + -0.2VSolution
x = {0, 10 + -0.2V}
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