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Simplifying (2x2 + -4x + 7) + -1(-3x2 + 4x + -5) = 0 Reorder the terms: (7 + -4x + 2x2) + -1(-3x2 + 4x + -5) = 0 Remove parenthesis around (7 + -4x + 2x2) 7 + -4x + 2x2 + -1(-3x2 + 4x + -5) = 0 Reorder the terms: 7 + -4x + 2x2 + -1(-5 + 4x + -3x2) = 0 7 + -4x + 2x2 + (-5 * -1 + 4x * -1 + -3x2 * -1) = 0 7 + -4x + 2x2 + (5 + -4x + 3x2) = 0 Reorder the terms: 7 + 5 + -4x + -4x + 2x2 + 3x2 = 0 Combine like terms: 7 + 5 = 12 12 + -4x + -4x + 2x2 + 3x2 = 0 Combine like terms: -4x + -4x = -8x 12 + -8x + 2x2 + 3x2 = 0 Combine like terms: 2x2 + 3x2 = 5x2 12 + -8x + 5x2 = 0 Solving 12 + -8x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2.4 + -1.6x + x2 = 0 Move the constant term to the right: Add '-2.4' to each side of the equation. 2.4 + -1.6x + -2.4 + x2 = 0 + -2.4 Reorder the terms: 2.4 + -2.4 + -1.6x + x2 = 0 + -2.4 Combine like terms: 2.4 + -2.4 = 0.0 0.0 + -1.6x + x2 = 0 + -2.4 -1.6x + x2 = 0 + -2.4 Combine like terms: 0 + -2.4 = -2.4 -1.6x + x2 = -2.4 The x term is -1.6x. Take half its coefficient (-0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. -1.6x + 0.64 + x2 = -2.4 + 0.64 Reorder the terms: 0.64 + -1.6x + x2 = -2.4 + 0.64 Combine like terms: -2.4 + 0.64 = -1.76 0.64 + -1.6x + x2 = -1.76 Factor a perfect square on the left side: (x + -0.8)(x + -0.8) = -1.76 Can't calculate square root of the right side. The solution to this equation could not be determined.
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