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Simplifying (6x2 + 8x + 12) + -1(4x2 + 3x + -2) = 0 Reorder the terms: (12 + 8x + 6x2) + -1(4x2 + 3x + -2) = 0 Remove parenthesis around (12 + 8x + 6x2) 12 + 8x + 6x2 + -1(4x2 + 3x + -2) = 0 Reorder the terms: 12 + 8x + 6x2 + -1(-2 + 3x + 4x2) = 0 12 + 8x + 6x2 + (-2 * -1 + 3x * -1 + 4x2 * -1) = 0 12 + 8x + 6x2 + (2 + -3x + -4x2) = 0 Reorder the terms: 12 + 2 + 8x + -3x + 6x2 + -4x2 = 0 Combine like terms: 12 + 2 = 14 14 + 8x + -3x + 6x2 + -4x2 = 0 Combine like terms: 8x + -3x = 5x 14 + 5x + 6x2 + -4x2 = 0 Combine like terms: 6x2 + -4x2 = 2x2 14 + 5x + 2x2 = 0 Solving 14 + 5x + 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 + 2.5x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + 2.5x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 2.5x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2.5x + x2 = 0 + -7 2.5x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 2.5x + x2 = -7 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = -7 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = -7 + 1.5625 Combine like terms: -7 + 1.5625 = -5.4375 1.5625 + 2.5x + x2 = -5.4375 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = -5.4375 Can't calculate square root of the right side. The solution to this equation could not be determined.
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