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Simplifying 45 = 0.01x(120 + -1x) 45 = (120 * 0.01x + -1x * 0.01x) 45 = (1.2x + -0.01x2) Solving 45 = 1.2x + -0.01x2 Solving for variable 'x'. Reorder the terms: 45 + -1.2x + 0.01x2 = 1.2x + -1.2x + -0.01x2 + 0.01x2 Combine like terms: 1.2x + -1.2x = 0.0 45 + -1.2x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 45 + -1.2x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 45 + -1.2x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 4500 + -120x + x2 = 0 Move the constant term to the right: Add '-4500' to each side of the equation. 4500 + -120x + -4500 + x2 = 0 + -4500 Reorder the terms: 4500 + -4500 + -120x + x2 = 0 + -4500 Combine like terms: 4500 + -4500 = 0 0 + -120x + x2 = 0 + -4500 -120x + x2 = 0 + -4500 Combine like terms: 0 + -4500 = -4500 -120x + x2 = -4500 The x term is -120x. Take half its coefficient (-60). Square it (3600) and add it to both sides. Add '3600' to each side of the equation. -120x + 3600 + x2 = -4500 + 3600 Reorder the terms: 3600 + -120x + x2 = -4500 + 3600 Combine like terms: -4500 + 3600 = -900 3600 + -120x + x2 = -900 Factor a perfect square on the left side: (x + -60)(x + -60) = -900 Can't calculate square root of the right side. The solution to this equation could not be determined.
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