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Simplifying (4x + -5)(3 + -2x) = 12 + -9(2x + -5) Reorder the terms: (-5 + 4x)(3 + -2x) = 12 + -9(2x + -5) Multiply (-5 + 4x) * (3 + -2x) (-5(3 + -2x) + 4x * (3 + -2x)) = 12 + -9(2x + -5) ((3 * -5 + -2x * -5) + 4x * (3 + -2x)) = 12 + -9(2x + -5) ((-15 + 10x) + 4x * (3 + -2x)) = 12 + -9(2x + -5) (-15 + 10x + (3 * 4x + -2x * 4x)) = 12 + -9(2x + -5) (-15 + 10x + (12x + -8x2)) = 12 + -9(2x + -5) Combine like terms: 10x + 12x = 22x (-15 + 22x + -8x2) = 12 + -9(2x + -5) Reorder the terms: -15 + 22x + -8x2 = 12 + -9(-5 + 2x) -15 + 22x + -8x2 = 12 + (-5 * -9 + 2x * -9) -15 + 22x + -8x2 = 12 + (45 + -18x) Combine like terms: 12 + 45 = 57 -15 + 22x + -8x2 = 57 + -18x Solving -15 + 22x + -8x2 = 57 + -18x Solving for variable 'x'. Reorder the terms: -15 + -57 + 22x + 18x + -8x2 = 57 + -18x + -57 + 18x Combine like terms: -15 + -57 = -72 -72 + 22x + 18x + -8x2 = 57 + -18x + -57 + 18x Combine like terms: 22x + 18x = 40x -72 + 40x + -8x2 = 57 + -18x + -57 + 18x Reorder the terms: -72 + 40x + -8x2 = 57 + -57 + -18x + 18x Combine like terms: 57 + -57 = 0 -72 + 40x + -8x2 = 0 + -18x + 18x -72 + 40x + -8x2 = -18x + 18x Combine like terms: -18x + 18x = 0 -72 + 40x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-9 + 5x + -1x2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-9 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -9 + 5x + -1x2 = 0 Solving -9 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 9 + -5x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -5x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -5x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x + x2 = 0 + -9 -5x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -5x + x2 = -9 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -9 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -9 + 6.25 Combine like terms: -9 + 6.25 = -2.75 6.25 + -5x + x2 = -2.75 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -2.75 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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