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Simplifying 3x + 5 = 4x2 + 20 Reorder the terms: 5 + 3x = 4x2 + 20 Reorder the terms: 5 + 3x = 20 + 4x2 Solving 5 + 3x = 20 + 4x2 Solving for variable 'x'. Reorder the terms: 5 + -20 + 3x + -4x2 = 20 + 4x2 + -20 + -4x2 Combine like terms: 5 + -20 = -15 -15 + 3x + -4x2 = 20 + 4x2 + -20 + -4x2 Reorder the terms: -15 + 3x + -4x2 = 20 + -20 + 4x2 + -4x2 Combine like terms: 20 + -20 = 0 -15 + 3x + -4x2 = 0 + 4x2 + -4x2 -15 + 3x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -15 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.75 + -0.75x + x2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + -0.75x + -3.75 + x2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + -0.75x + x2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + -0.75x + x2 = 0 + -3.75 -0.75x + x2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 -0.75x + x2 = -3.75 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 = -3.75 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -3.75 + 0.140625 Combine like terms: -3.75 + 0.140625 = -3.609375 0.140625 + -0.75x + x2 = -3.609375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -3.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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