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Simplifying (6x2 + -5x + 8) + -1(x2 + 7x + -1) = 0 Reorder the terms: (8 + -5x + 6x2) + -1(x2 + 7x + -1) = 0 Remove parenthesis around (8 + -5x + 6x2) 8 + -5x + 6x2 + -1(x2 + 7x + -1) = 0 Reorder the terms: 8 + -5x + 6x2 + -1(-1 + 7x + x2) = 0 8 + -5x + 6x2 + (-1 * -1 + 7x * -1 + x2 * -1) = 0 8 + -5x + 6x2 + (1 + -7x + -1x2) = 0 Reorder the terms: 8 + 1 + -5x + -7x + 6x2 + -1x2 = 0 Combine like terms: 8 + 1 = 9 9 + -5x + -7x + 6x2 + -1x2 = 0 Combine like terms: -5x + -7x = -12x 9 + -12x + 6x2 + -1x2 = 0 Combine like terms: 6x2 + -1x2 = 5x2 9 + -12x + 5x2 = 0 Solving 9 + -12x + 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'. 1.8 + -2.4x + x2 = 0 Move the constant term to the right: Add '-1.8' to each side of the equation. 1.8 + -2.4x + -1.8 + x2 = 0 + -1.8 Reorder the terms: 1.8 + -1.8 + -2.4x + x2 = 0 + -1.8 Combine like terms: 1.8 + -1.8 = 0.0 0.0 + -2.4x + x2 = 0 + -1.8 -2.4x + x2 = 0 + -1.8 Combine like terms: 0 + -1.8 = -1.8 -2.4x + x2 = -1.8 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -1.8 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -1.8 + 1.44 Combine like terms: -1.8 + 1.44 = -0.36 1.44 + -2.4x + x2 = -0.36 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = -0.36 Can't calculate square root of the right side. The solution to this equation could not be determined.
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