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Simplifying f(0) = 0.03x2 + 0.06x + 30.4 Reorder the terms for easier multiplication: 0f = 0.03x2 + 0.06x + 30.4 Anything times zero is zero. 0f = 0.03x2 + 0.06x + 30.4 Reorder the terms: 0 = 30.4 + 0.06x + 0.03x2 Solving 0 = 30.4 + 0.06x + 0.03x2 Solving for variable 'x'. Combine like terms: 0 + -30.4 = -30.4 -30.4 + -0.06x + -0.03x2 = 30.4 + 0.06x + 0.03x2 + -30.4 + -0.06x + -0.03x2 Reorder the terms: -30.4 + -0.06x + -0.03x2 = 30.4 + -30.4 + 0.06x + -0.06x + 0.03x2 + -0.03x2 Combine like terms: 30.4 + -30.4 = 0.0 -30.4 + -0.06x + -0.03x2 = 0.0 + 0.06x + -0.06x + 0.03x2 + -0.03x2 -30.4 + -0.06x + -0.03x2 = 0.06x + -0.06x + 0.03x2 + -0.03x2 Combine like terms: 0.06x + -0.06x = 0.00 -30.4 + -0.06x + -0.03x2 = 0.00 + 0.03x2 + -0.03x2 -30.4 + -0.06x + -0.03x2 = 0.03x2 + -0.03x2 Combine like terms: 0.03x2 + -0.03x2 = 0.00 -30.4 + -0.06x + -0.03x2 = 0.00 Begin completing the square. Divide all terms by -0.03 the coefficient of the squared term: Divide each side by '-0.03'. 1013.333333 + 2x + x2 = 0 Move the constant term to the right: Add '-1013.333333' to each side of the equation. 1013.333333 + 2x + -1013.333333 + x2 = 0 + -1013.333333 Reorder the terms: 1013.333333 + -1013.333333 + 2x + x2 = 0 + -1013.333333 Combine like terms: 1013.333333 + -1013.333333 = 0.000000 0.000000 + 2x + x2 = 0 + -1013.333333 2x + x2 = 0 + -1013.333333 Combine like terms: 0 + -1013.333333 = -1013.333333 2x + x2 = -1013.333333 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 = -1013.333333 + 1 Reorder the terms: 1 + 2x + x2 = -1013.333333 + 1 Combine like terms: -1013.333333 + 1 = -1012.333333 1 + 2x + x2 = -1012.333333 Factor a perfect square on the left side: (x + 1)(x + 1) = -1012.333333 Can't calculate square root of the right side. The solution to this equation could not be determined.
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