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Simplifying (x2 + -0.4x) = 1 + -1(0.3x + 1) Reorder the terms: (-0.4x + x2) = 1 + -1(0.3x + 1) Remove parenthesis around (-0.4x + x2) -0.4x + x2 = 1 + -1(0.3x + 1) Reorder the terms: -0.4x + x2 = 1 + -1(1 + 0.3x) -0.4x + x2 = 1 + (1 * -1 + 0.3x * -1) -0.4x + x2 = 1 + (-1 + -0.3x) Combine like terms: 1 + -1 = 0 -0.4x + x2 = 0 + -0.3x -0.4x + x2 = -0.3x Solving -0.4x + x2 = -0.3x Solving for variable 'x'. Reorder the terms: -0.4x + 0.3x + x2 = -0.3x + 0.3x Combine like terms: -0.4x + 0.3x = -0.1x -0.1x + x2 = -0.3x + 0.3x Combine like terms: -0.3x + 0.3x = 0.0 -0.1x + x2 = 0.0 Factor out the Greatest Common Factor (GCF), 'x'. x(-0.1 + x) = 0.0Subproblem 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 '(-0.1 + x)' equal to zero and attempt to solve: Simplifying -0.1 + x = 0 Solving -0.1 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '0.1' to each side of the equation. -0.1 + 0.1 + x = 0 + 0.1 Combine like terms: -0.1 + 0.1 = 0.0 0.0 + x = 0 + 0.1 x = 0 + 0.1 Combine like terms: 0 + 0.1 = 0.1 x = 0.1 Simplifying x = 0.1Solution
x = {0, 0.1}
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