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Simplifying 0.75 = 0.05x2 + 0.2x + 1 Reorder the terms: 0.75 = 1 + 0.2x + 0.05x2 Solving 0.75 = 1 + 0.2x + 0.05x2 Solving for variable 'x'. Combine like terms: 0.75 + -1 = -0.25 -0.25 + -0.2x + -0.05x2 = 1 + 0.2x + 0.05x2 + -1 + -0.2x + -0.05x2 Reorder the terms: -0.25 + -0.2x + -0.05x2 = 1 + -1 + 0.2x + -0.2x + 0.05x2 + -0.05x2 Combine like terms: 1 + -1 = 0 -0.25 + -0.2x + -0.05x2 = 0 + 0.2x + -0.2x + 0.05x2 + -0.05x2 -0.25 + -0.2x + -0.05x2 = 0.2x + -0.2x + 0.05x2 + -0.05x2 Combine like terms: 0.2x + -0.2x = 0.0 -0.25 + -0.2x + -0.05x2 = 0.0 + 0.05x2 + -0.05x2 -0.25 + -0.2x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 -0.25 + -0.2x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. 5 + 4x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + 4x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + 4x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x + x2 = 0 + -5 4x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 4x + x2 = -5 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = -5 + 4 Reorder the terms: 4 + 4x + x2 = -5 + 4 Combine like terms: -5 + 4 = -1 4 + 4x + x2 = -1 Factor a perfect square on the left side: (x + 2)(x + 2) = -1 Can't calculate square root of the right side. The solution to this equation could not be determined.
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