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Simplifying 0 = 450 + 0.1x2 + -0.2x Reorder the terms: 0 = 450 + -0.2x + 0.1x2 Solving 0 = 450 + -0.2x + 0.1x2 Solving for variable 'x'. Combine like terms: 0 + -450 = -450 -450 + 0.2x + -0.1x2 = 450 + -0.2x + 0.1x2 + -450 + 0.2x + -0.1x2 Reorder the terms: -450 + 0.2x + -0.1x2 = 450 + -450 + -0.2x + 0.2x + 0.1x2 + -0.1x2 Combine like terms: 450 + -450 = 0 -450 + 0.2x + -0.1x2 = 0 + -0.2x + 0.2x + 0.1x2 + -0.1x2 -450 + 0.2x + -0.1x2 = -0.2x + 0.2x + 0.1x2 + -0.1x2 Combine like terms: -0.2x + 0.2x = 0.0 -450 + 0.2x + -0.1x2 = 0.0 + 0.1x2 + -0.1x2 -450 + 0.2x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -450 + 0.2x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 4500 + -2x + x2 = 0 Move the constant term to the right: Add '-4500' to each side of the equation. 4500 + -2x + -4500 + x2 = 0 + -4500 Reorder the terms: 4500 + -4500 + -2x + x2 = 0 + -4500 Combine like terms: 4500 + -4500 = 0 0 + -2x + x2 = 0 + -4500 -2x + x2 = 0 + -4500 Combine like terms: 0 + -4500 = -4500 -2x + x2 = -4500 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = -4500 + 1 Reorder the terms: 1 + -2x + x2 = -4500 + 1 Combine like terms: -4500 + 1 = -4499 1 + -2x + x2 = -4499 Factor a perfect square on the left side: (x + -1)(x + -1) = -4499 Can't calculate square root of the right side. The solution to this equation could not be determined.
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