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Simplifying (x + 1)(3x + 5) = 2x + -1(7 + -3x) Reorder the terms: (1 + x)(3x + 5) = 2x + -1(7 + -3x) Reorder the terms: (1 + x)(5 + 3x) = 2x + -1(7 + -3x) Multiply (1 + x) * (5 + 3x) (1(5 + 3x) + x(5 + 3x)) = 2x + -1(7 + -3x) ((5 * 1 + 3x * 1) + x(5 + 3x)) = 2x + -1(7 + -3x) ((5 + 3x) + x(5 + 3x)) = 2x + -1(7 + -3x) (5 + 3x + (5 * x + 3x * x)) = 2x + -1(7 + -3x) (5 + 3x + (5x + 3x2)) = 2x + -1(7 + -3x) Combine like terms: 3x + 5x = 8x (5 + 8x + 3x2) = 2x + -1(7 + -3x) 5 + 8x + 3x2 = 2x + (7 * -1 + -3x * -1) 5 + 8x + 3x2 = 2x + (-7 + 3x) Reorder the terms: 5 + 8x + 3x2 = -7 + 2x + 3x Combine like terms: 2x + 3x = 5x 5 + 8x + 3x2 = -7 + 5x Solving 5 + 8x + 3x2 = -7 + 5x Solving for variable 'x'. Reorder the terms: 5 + 7 + 8x + -5x + 3x2 = -7 + 5x + 7 + -5x Combine like terms: 5 + 7 = 12 12 + 8x + -5x + 3x2 = -7 + 5x + 7 + -5x Combine like terms: 8x + -5x = 3x 12 + 3x + 3x2 = -7 + 5x + 7 + -5x Reorder the terms: 12 + 3x + 3x2 = -7 + 7 + 5x + -5x Combine like terms: -7 + 7 = 0 12 + 3x + 3x2 = 0 + 5x + -5x 12 + 3x + 3x2 = 5x + -5x Combine like terms: 5x + -5x = 0 12 + 3x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + x + x2)' equal to zero and attempt to solve: Simplifying 4 + x + x2 = 0 Solving 4 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x + x2 = 0 + -4 x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 x + x2 = -4 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. x + 0.25 + x2 = -4 + 0.25 Reorder the terms: 0.25 + x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + x + x2 = -3.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -3.75 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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