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Simplifying f(0) = 4x2 + -3x + 3 Reorder the terms for easier multiplication: 0f = 4x2 + -3x + 3 Anything times zero is zero. 0f = 4x2 + -3x + 3 Reorder the terms: 0 = 3 + -3x + 4x2 Solving 0 = 3 + -3x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + 3x + -4x2 = 3 + -3x + 4x2 + -3 + 3x + -4x2 Reorder the terms: -3 + 3x + -4x2 = 3 + -3 + -3x + 3x + 4x2 + -4x2 Combine like terms: 3 + -3 = 0 -3 + 3x + -4x2 = 0 + -3x + 3x + 4x2 + -4x2 -3 + 3x + -4x2 = -3x + 3x + 4x2 + -4x2 Combine like terms: -3x + 3x = 0 -3 + 3x + -4x2 = 0 + 4x2 + -4x2 -3 + 3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -3 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 0.75 + -0.75x + x2 = 0 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -0.75x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -0.75x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -0.75x + x2 = 0 + -0.75 -0.75x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -0.75x + x2 = -0.75 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.75 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.75 + 0.140625 Combine like terms: -0.75 + 0.140625 = -0.609375 0.140625 + -0.75x + x2 = -0.609375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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