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Simplifying (5x2 + -3x + 6) + -1(3x2 + 4x + -7) = 0 Reorder the terms: (6 + -3x + 5x2) + -1(3x2 + 4x + -7) = 0 Remove parenthesis around (6 + -3x + 5x2) 6 + -3x + 5x2 + -1(3x2 + 4x + -7) = 0 Reorder the terms: 6 + -3x + 5x2 + -1(-7 + 4x + 3x2) = 0 6 + -3x + 5x2 + (-7 * -1 + 4x * -1 + 3x2 * -1) = 0 6 + -3x + 5x2 + (7 + -4x + -3x2) = 0 Reorder the terms: 6 + 7 + -3x + -4x + 5x2 + -3x2 = 0 Combine like terms: 6 + 7 = 13 13 + -3x + -4x + 5x2 + -3x2 = 0 Combine like terms: -3x + -4x = -7x 13 + -7x + 5x2 + -3x2 = 0 Combine like terms: 5x2 + -3x2 = 2x2 13 + -7x + 2x2 = 0 Solving 13 + -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'. 6.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '-6.5' to each side of the equation. 6.5 + -3.5x + -6.5 + x2 = 0 + -6.5 Reorder the terms: 6.5 + -6.5 + -3.5x + x2 = 0 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + -3.5x + x2 = 0 + -6.5 -3.5x + x2 = 0 + -6.5 Combine like terms: 0 + -6.5 = -6.5 -3.5x + x2 = -6.5 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 = -6.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = -6.5 + 3.0625 Combine like terms: -6.5 + 3.0625 = -3.4375 3.0625 + -3.5x + x2 = -3.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = -3.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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