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Simplifying (x + -3) + -1(5 + -3x) = 2x(x + 1) Reorder the terms: (-3 + x) + -1(5 + -3x) = 2x(x + 1) Remove parenthesis around (-3 + x) -3 + x + -1(5 + -3x) = 2x(x + 1) -3 + x + (5 * -1 + -3x * -1) = 2x(x + 1) -3 + x + (-5 + 3x) = 2x(x + 1) Reorder the terms: -3 + -5 + x + 3x = 2x(x + 1) Combine like terms: -3 + -5 = -8 -8 + x + 3x = 2x(x + 1) Combine like terms: x + 3x = 4x -8 + 4x = 2x(x + 1) Reorder the terms: -8 + 4x = 2x(1 + x) -8 + 4x = (1 * 2x + x * 2x) -8 + 4x = (2x + 2x2) Solving -8 + 4x = 2x + 2x2 Solving for variable 'x'. Combine like terms: 4x + -2x = 2x -8 + 2x + -2x2 = 2x + 2x2 + -2x + -2x2 Reorder the terms: -8 + 2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 -8 + 2x + -2x2 = 0 + 2x2 + -2x2 -8 + 2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + 2x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + x + -1x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4 + x + -1x2)' equal to zero and attempt to solve: Simplifying -4 + x + -1x2 = 0 Solving -4 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 4 + -1x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -1x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -1x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x + x2 = 0 + -4 -1x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -1x + 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. -1x + 0.25 + x2 = -4 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -4 + 0.25 Combine like terms: -4 + 0.25 = -3.75 0.25 + -1x + 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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