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Simplifying 2x + (3x2 + -6x + 7 + -5 + 3x2 + 6) + -1(4x2 + -7x + -6) = 0 Reorder the terms: 2x + (7 + -5 + 6 + -6x + 3x2 + 3x2) + -1(4x2 + -7x + -6) = 0 Combine like terms: 7 + -5 = 2 2x + (2 + 6 + -6x + 3x2 + 3x2) + -1(4x2 + -7x + -6) = 0 Combine like terms: 2 + 6 = 8 2x + (8 + -6x + 3x2 + 3x2) + -1(4x2 + -7x + -6) = 0 Combine like terms: 3x2 + 3x2 = 6x2 2x + (8 + -6x + 6x2) + -1(4x2 + -7x + -6) = 0 Remove parenthesis around (8 + -6x + 6x2) 2x + 8 + -6x + 6x2 + -1(4x2 + -7x + -6) = 0 Reorder the terms: 2x + 8 + -6x + 6x2 + -1(-6 + -7x + 4x2) = 0 2x + 8 + -6x + 6x2 + (-6 * -1 + -7x * -1 + 4x2 * -1) = 0 2x + 8 + -6x + 6x2 + (6 + 7x + -4x2) = 0 Reorder the terms: 8 + 6 + 2x + -6x + 7x + 6x2 + -4x2 = 0 Combine like terms: 8 + 6 = 14 14 + 2x + -6x + 7x + 6x2 + -4x2 = 0 Combine like terms: 2x + -6x = -4x 14 + -4x + 7x + 6x2 + -4x2 = 0 Combine like terms: -4x + 7x = 3x 14 + 3x + 6x2 + -4x2 = 0 Combine like terms: 6x2 + -4x2 = 2x2 14 + 3x + 2x2 = 0 Solving 14 + 3x + 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'. 7 + 1.5x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 1.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 1.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 1.5x + x2 = 0 + -7 1.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 1.5x + x2 = -7 The x term is 1.5x. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5x + 0.5625 + x2 = -7 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -7 + 0.5625 Combine like terms: -7 + 0.5625 = -6.4375 0.5625 + 1.5x + x2 = -6.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -6.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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