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Simplifying M(x) = -2x2 + 10x Multiply M * x xM = -2x2 + 10x Reorder the terms: xM = 10x + -2x2 Solving xM = 10x + -2x2 Solving for variable 'x'. Reorder the terms: -10x + xM + 2x2 = 10x + -2x2 + -10x + 2x2 Reorder the terms: -10x + xM + 2x2 = 10x + -10x + -2x2 + 2x2 Combine like terms: 10x + -10x = 0 -10x + xM + 2x2 = 0 + -2x2 + 2x2 -10x + xM + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -10x + xM + 2x2 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(-10 + M + 2x) = 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 '(-10 + M + 2x)' equal to zero and attempt to solve: Simplifying -10 + M + 2x = 0 Solving -10 + M + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + M + 10 + 2x = 0 + 10 Reorder the terms: -10 + 10 + M + 2x = 0 + 10 Combine like terms: -10 + 10 = 0 0 + M + 2x = 0 + 10 M + 2x = 0 + 10 Combine like terms: 0 + 10 = 10 M + 2x = 10 Add '-1M' to each side of the equation. M + -1M + 2x = 10 + -1M Combine like terms: M + -1M = 0 0 + 2x = 10 + -1M 2x = 10 + -1M Divide each side by '2'. x = 5 + -0.5M Simplifying x = 5 + -0.5MSolution
x = {0, 5 + -0.5M}
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