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Simplifying 100 = 0.1x(30 + -1x) 100 = (30 * 0.1x + -1x * 0.1x) 100 = (3x + -0.1x2) Solving 100 = 3x + -0.1x2 Solving for variable 'x'. Reorder the terms: 100 + -3x + 0.1x2 = 3x + -3x + -0.1x2 + 0.1x2 Combine like terms: 3x + -3x = 0 100 + -3x + 0.1x2 = 0 + -0.1x2 + 0.1x2 100 + -3x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 100 + -3x + 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'. 1000 + -30x + x2 = 0 Move the constant term to the right: Add '-1000' to each side of the equation. 1000 + -30x + -1000 + x2 = 0 + -1000 Reorder the terms: 1000 + -1000 + -30x + x2 = 0 + -1000 Combine like terms: 1000 + -1000 = 0 0 + -30x + x2 = 0 + -1000 -30x + x2 = 0 + -1000 Combine like terms: 0 + -1000 = -1000 -30x + x2 = -1000 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -1000 + 225 Reorder the terms: 225 + -30x + x2 = -1000 + 225 Combine like terms: -1000 + 225 = -775 225 + -30x + x2 = -775 Factor a perfect square on the left side: (x + -15)(x + -15) = -775 Can't calculate square root of the right side. The solution to this equation could not be determined.
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