M(x)=20x-x^2

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Solution for M(x)=20x-x^2 equation:


Simplifying
M(x) = 20x + -1x2

Multiply M * x
xM = 20x + -1x2

Solving
xM = 20x + -1x2

Solving for variable 'x'.

Reorder the terms:
-20x + xM + x2 = 20x + -1x2 + -20x + x2

Reorder the terms:
-20x + xM + x2 = 20x + -20x + -1x2 + x2

Combine like terms: 20x + -20x = 0
-20x + xM + x2 = 0 + -1x2 + x2
-20x + xM + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-20x + xM + x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-20 + M + x) = 0

Subproblem 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 = 0

Subproblem 2

Set the factor '(-20 + M + x)' equal to zero and attempt to solve: Simplifying -20 + M + x = 0 Solving -20 + M + x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + M + 20 + x = 0 + 20 Reorder the terms: -20 + 20 + M + x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + M + x = 0 + 20 M + x = 0 + 20 Combine like terms: 0 + 20 = 20 M + x = 20 Add '-1M' to each side of the equation. M + -1M + x = 20 + -1M Combine like terms: M + -1M = 0 0 + x = 20 + -1M x = 20 + -1M Simplifying x = 20 + -1M

Solution

x = {0, 20 + -1M}

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