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Simplifying 2.5(x) = 2x2 + -3x + 7 Reorder the terms: 2.5x = 7 + -3x + 2x2 Solving 2.5x = 7 + -3x + 2x2 Solving for variable 'x'. Reorder the terms: -7 + 2.5x + 3x + -2x2 = 7 + -3x + 2x2 + -7 + 3x + -2x2 Combine like terms: 2.5x + 3x = 5.5x -7 + 5.5x + -2x2 = 7 + -3x + 2x2 + -7 + 3x + -2x2 Reorder the terms: -7 + 5.5x + -2x2 = 7 + -7 + -3x + 3x + 2x2 + -2x2 Combine like terms: 7 + -7 = 0 -7 + 5.5x + -2x2 = 0 + -3x + 3x + 2x2 + -2x2 -7 + 5.5x + -2x2 = -3x + 3x + 2x2 + -2x2 Combine like terms: -3x + 3x = 0 -7 + 5.5x + -2x2 = 0 + 2x2 + -2x2 -7 + 5.5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -7 + 5.5x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 3.5 + -2.75x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -2.75x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -2.75x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -2.75x + x2 = 0 + -3.5 -2.75x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -2.75x + x2 = -3.5 The x term is -2.75x. Take half its coefficient (-1.375). Square it (1.890625) and add it to both sides. Add '1.890625' to each side of the equation. -2.75x + 1.890625 + x2 = -3.5 + 1.890625 Reorder the terms: 1.890625 + -2.75x + x2 = -3.5 + 1.890625 Combine like terms: -3.5 + 1.890625 = -1.609375 1.890625 + -2.75x + x2 = -1.609375 Factor a perfect square on the left side: (x + -1.375)(x + -1.375) = -1.609375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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