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Simplifying (3x + -1)(2 + -1x) + -1x(x + 3) = 2 Reorder the terms: (-1 + 3x)(2 + -1x) + -1x(x + 3) = 2 Multiply (-1 + 3x) * (2 + -1x) (-1(2 + -1x) + 3x * (2 + -1x)) + -1x(x + 3) = 2 ((2 * -1 + -1x * -1) + 3x * (2 + -1x)) + -1x(x + 3) = 2 ((-2 + 1x) + 3x * (2 + -1x)) + -1x(x + 3) = 2 (-2 + 1x + (2 * 3x + -1x * 3x)) + -1x(x + 3) = 2 (-2 + 1x + (6x + -3x2)) + -1x(x + 3) = 2 Combine like terms: 1x + 6x = 7x (-2 + 7x + -3x2) + -1x(x + 3) = 2 Reorder the terms: -2 + 7x + -3x2 + -1x(3 + x) = 2 -2 + 7x + -3x2 + (3 * -1x + x * -1x) = 2 -2 + 7x + -3x2 + (-3x + -1x2) = 2 Reorder the terms: -2 + 7x + -3x + -3x2 + -1x2 = 2 Combine like terms: 7x + -3x = 4x -2 + 4x + -3x2 + -1x2 = 2 Combine like terms: -3x2 + -1x2 = -4x2 -2 + 4x + -4x2 = 2 Solving -2 + 4x + -4x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -2 + 4x + -4x2 = 2 + -2 Combine like terms: -2 + -2 = -4 -4 + 4x + -4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -4 + 4x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-1 + x + -1x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + x + -1x2)' equal to zero and attempt to solve: Simplifying -1 + x + -1x2 = 0 Solving -1 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 1 + -1x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + -1x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x + x2 = 0 + -1 -1x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1x + x2 = -1 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -1 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -1 + 0.25 Combine like terms: -1 + 0.25 = -0.75 0.25 + -1x + x2 = -0.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.75 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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