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Simplifying 2(3x + 3) + -4(5x + -3) = x(-1x + -13) + -1x(x + -5) Reorder the terms: 2(3 + 3x) + -4(5x + -3) = x(-1x + -13) + -1x(x + -5) (3 * 2 + 3x * 2) + -4(5x + -3) = x(-1x + -13) + -1x(x + -5) (6 + 6x) + -4(5x + -3) = x(-1x + -13) + -1x(x + -5) Reorder the terms: 6 + 6x + -4(-3 + 5x) = x(-1x + -13) + -1x(x + -5) 6 + 6x + (-3 * -4 + 5x * -4) = x(-1x + -13) + -1x(x + -5) 6 + 6x + (12 + -20x) = x(-1x + -13) + -1x(x + -5) Reorder the terms: 6 + 12 + 6x + -20x = x(-1x + -13) + -1x(x + -5) Combine like terms: 6 + 12 = 18 18 + 6x + -20x = x(-1x + -13) + -1x(x + -5) Combine like terms: 6x + -20x = -14x 18 + -14x = x(-1x + -13) + -1x(x + -5) Reorder the terms: 18 + -14x = x(-13 + -1x) + -1x(x + -5) 18 + -14x = (-13 * x + -1x * x) + -1x(x + -5) 18 + -14x = (-13x + -1x2) + -1x(x + -5) Reorder the terms: 18 + -14x = -13x + -1x2 + -1x(-5 + x) 18 + -14x = -13x + -1x2 + (-5 * -1x + x * -1x) 18 + -14x = -13x + -1x2 + (5x + -1x2) Reorder the terms: 18 + -14x = -13x + 5x + -1x2 + -1x2 Combine like terms: -13x + 5x = -8x 18 + -14x = -8x + -1x2 + -1x2 Combine like terms: -1x2 + -1x2 = -2x2 18 + -14x = -8x + -2x2 Solving 18 + -14x = -8x + -2x2 Solving for variable 'x'. Combine like terms: -14x + 8x = -6x 18 + -6x + 2x2 = -8x + -2x2 + 8x + 2x2 Reorder the terms: 18 + -6x + 2x2 = -8x + 8x + -2x2 + 2x2 Combine like terms: -8x + 8x = 0 18 + -6x + 2x2 = 0 + -2x2 + 2x2 18 + -6x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 18 + -6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(9 + -3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(9 + -3x + x2)' equal to zero and attempt to solve: Simplifying 9 + -3x + x2 = 0 Solving 9 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + -3x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -3x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -3x + x2 = 0 + -9 -3x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -3x + x2 = -9 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 = -9 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -9 + 2.25 Combine like terms: -9 + 2.25 = -6.75 2.25 + -3x + x2 = -6.75 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = -6.75 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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