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Simplifying (3x2 + -5x + 7) + -1(x2 + 2x + -3) = 0 Reorder the terms: (7 + -5x + 3x2) + -1(x2 + 2x + -3) = 0 Remove parenthesis around (7 + -5x + 3x2) 7 + -5x + 3x2 + -1(x2 + 2x + -3) = 0 Reorder the terms: 7 + -5x + 3x2 + -1(-3 + 2x + x2) = 0 7 + -5x + 3x2 + (-3 * -1 + 2x * -1 + x2 * -1) = 0 7 + -5x + 3x2 + (3 + -2x + -1x2) = 0 Reorder the terms: 7 + 3 + -5x + -2x + 3x2 + -1x2 = 0 Combine like terms: 7 + 3 = 10 10 + -5x + -2x + 3x2 + -1x2 = 0 Combine like terms: -5x + -2x = -7x 10 + -7x + 3x2 + -1x2 = 0 Combine like terms: 3x2 + -1x2 = 2x2 10 + -7x + 2x2 = 0 Solving 10 + -7x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -3.5x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -3.5x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3.5x + x2 = 0 + -5 -3.5x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -3.5x + x2 = -5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = -5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -5 + 3.0625 Combine like terms: -5 + 3.0625 = -1.9375 3.0625 + -3.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -1.9375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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