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Simplifying 0 = 4x2 + -5x + 12 Reorder the terms: 0 = 12 + -5x + 4x2 Solving 0 = 12 + -5x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -12 = -12 -12 + 5x + -4x2 = 12 + -5x + 4x2 + -12 + 5x + -4x2 Reorder the terms: -12 + 5x + -4x2 = 12 + -12 + -5x + 5x + 4x2 + -4x2 Combine like terms: 12 + -12 = 0 -12 + 5x + -4x2 = 0 + -5x + 5x + 4x2 + -4x2 -12 + 5x + -4x2 = -5x + 5x + 4x2 + -4x2 Combine like terms: -5x + 5x = 0 -12 + 5x + -4x2 = 0 + 4x2 + -4x2 -12 + 5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -12 + 5x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3 + -1.25x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -1.25x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -1.25x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1.25x + x2 = 0 + -3 -1.25x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -1.25x + x2 = -3 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -3 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -3 + 0.390625 Combine like terms: -3 + 0.390625 = -2.609375 0.390625 + -1.25x + x2 = -2.609375 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = -2.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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