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Simplifying 0 = 0.5x3 + -1x Reorder the terms: 0 = -1x + 0.5x3 Solving 0 = -1x + 0.5x3 Solving for variable 'x'. Remove the zero: x + -0.5x3 = -1x + 0.5x3 + x + -0.5x3 Reorder the terms: x + -0.5x3 = -1x + x + 0.5x3 + -0.5x3 Combine like terms: -1x + x = 0 x + -0.5x3 = 0 + 0.5x3 + -0.5x3 x + -0.5x3 = 0.5x3 + -0.5x3 Combine like terms: 0.5x3 + -0.5x3 = 0.0 x + -0.5x3 = 0.0 Factor out the Greatest Common Factor (GCF), 'x'. x(1 + -0.5x2) = 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 '(1 + -0.5x2)' equal to zero and attempt to solve: Simplifying 1 + -0.5x2 = 0 Solving 1 + -0.5x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -0.5x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -0.5x2 = 0 + -1 -0.5x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -0.5x2 = -1 Divide each side by '-0.5'. x2 = 2 Simplifying x2 = 2 Take the square root of each side: x = {-1.414213562, 1.414213562}Solution
x = {0, -1.414213562, 1.414213562}
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