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Simplifying (4x + -5)(3 + -2x) = 4 + -1(2x + -7) Reorder the terms: (-5 + 4x)(3 + -2x) = 4 + -1(2x + -7) Multiply (-5 + 4x) * (3 + -2x) (-5(3 + -2x) + 4x * (3 + -2x)) = 4 + -1(2x + -7) ((3 * -5 + -2x * -5) + 4x * (3 + -2x)) = 4 + -1(2x + -7) ((-15 + 10x) + 4x * (3 + -2x)) = 4 + -1(2x + -7) (-15 + 10x + (3 * 4x + -2x * 4x)) = 4 + -1(2x + -7) (-15 + 10x + (12x + -8x2)) = 4 + -1(2x + -7) Combine like terms: 10x + 12x = 22x (-15 + 22x + -8x2) = 4 + -1(2x + -7) Reorder the terms: -15 + 22x + -8x2 = 4 + -1(-7 + 2x) -15 + 22x + -8x2 = 4 + (-7 * -1 + 2x * -1) -15 + 22x + -8x2 = 4 + (7 + -2x) Combine like terms: 4 + 7 = 11 -15 + 22x + -8x2 = 11 + -2x Solving -15 + 22x + -8x2 = 11 + -2x Solving for variable 'x'. Reorder the terms: -15 + -11 + 22x + 2x + -8x2 = 11 + -2x + -11 + 2x Combine like terms: -15 + -11 = -26 -26 + 22x + 2x + -8x2 = 11 + -2x + -11 + 2x Combine like terms: 22x + 2x = 24x -26 + 24x + -8x2 = 11 + -2x + -11 + 2x Reorder the terms: -26 + 24x + -8x2 = 11 + -11 + -2x + 2x Combine like terms: 11 + -11 = 0 -26 + 24x + -8x2 = 0 + -2x + 2x -26 + 24x + -8x2 = -2x + 2x Combine like terms: -2x + 2x = 0 -26 + 24x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-13 + 12x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-13 + 12x + -4x2)' equal to zero and attempt to solve: Simplifying -13 + 12x + -4x2 = 0 Solving -13 + 12x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. 3.25 + -3x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -3x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -3x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -3x + x2 = 0 + -3.25 -3x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -3x + x2 = -3.25 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -3.25 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -3.25 + 2.25 Combine like terms: -3.25 + 2.25 = -1 2.25 + -3x + x2 = -1 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -1 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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