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Simplifying (2x + -1)((-2) + (-1x)) = 4 Reorder the terms: (-1 + 2x)((-2) + (-1x)) = 4 (-1 + 2x)(-2 + (-1x)) = 4 Multiply (-1 + 2x) * (-2 + (-1x)) (-1(-2 + (-1x)) + 2x * (-2 + (-1x))) = 4 ((-2 * -1 + (-1x) * -1) + 2x * (-2 + (-1x))) = 4 ((2 + 1x) + 2x * (-2 + (-1x))) = 4 (2 + 1x + (-2 * 2x + (-1x) * 2x)) = 4 (2 + 1x + (-4x + -2x2)) = 4 Combine like terms: 1x + -4x = -3x (2 + -3x + -2x2) = 4 Solving 2 + -3x + -2x2 = 4 Solving for variable 'x'. Reorder the terms: 2 + -4 + -3x + -2x2 = 4 + -4 Combine like terms: 2 + -4 = -2 -2 + -3x + -2x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -2 + -3x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(2 + 3x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(2 + 3x + 2x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + 2x2 = 0 Solving 2 + 3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 1 + 1.5x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.5x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.5x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.5x + x2 = 0 + -1 1.5x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.5x + x2 = -1 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 = -1 + 0.5625 Reorder the terms: 0.5625 + 1.5x + x2 = -1 + 0.5625 Combine like terms: -1 + 0.5625 = -0.4375 0.5625 + 1.5x + x2 = -0.4375 Factor a perfect square on the left side: (x + 0.75)(x + 0.75) = -0.4375 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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