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Simplifying U(x) = 49x + -4x2 Multiply U * x xU = 49x + -4x2 Solving xU = 49x + -4x2 Solving for variable 'x'. Reorder the terms: -49x + xU + 4x2 = 49x + -4x2 + -49x + 4x2 Reorder the terms: -49x + xU + 4x2 = 49x + -49x + -4x2 + 4x2 Combine like terms: 49x + -49x = 0 -49x + xU + 4x2 = 0 + -4x2 + 4x2 -49x + xU + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -49x + xU + 4x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-49 + U + 4x) = 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 '(-49 + U + 4x)' equal to zero and attempt to solve: Simplifying -49 + U + 4x = 0 Solving -49 + U + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '49' to each side of the equation. -49 + U + 49 + 4x = 0 + 49 Reorder the terms: -49 + 49 + U + 4x = 0 + 49 Combine like terms: -49 + 49 = 0 0 + U + 4x = 0 + 49 U + 4x = 0 + 49 Combine like terms: 0 + 49 = 49 U + 4x = 49 Add '-1U' to each side of the equation. U + -1U + 4x = 49 + -1U Combine like terms: U + -1U = 0 0 + 4x = 49 + -1U 4x = 49 + -1U Divide each side by '4'. x = 12.25 + -0.25U Simplifying x = 12.25 + -0.25USolution
x = {0, 12.25 + -0.25U}
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