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Simplifying 12x(x + 3) = -3(x + 13) Reorder the terms: 12x(3 + x) = -3(x + 13) (3 * 12x + x * 12x) = -3(x + 13) (36x + 12x2) = -3(x + 13) Reorder the terms: 36x + 12x2 = -3(13 + x) 36x + 12x2 = (13 * -3 + x * -3) 36x + 12x2 = (-39 + -3x) Solving 36x + 12x2 = -39 + -3x Solving for variable 'x'. Reorder the terms: 39 + 36x + 3x + 12x2 = -39 + -3x + 39 + 3x Combine like terms: 36x + 3x = 39x 39 + 39x + 12x2 = -39 + -3x + 39 + 3x Reorder the terms: 39 + 39x + 12x2 = -39 + 39 + -3x + 3x Combine like terms: -39 + 39 = 0 39 + 39x + 12x2 = 0 + -3x + 3x 39 + 39x + 12x2 = -3x + 3x Combine like terms: -3x + 3x = 0 39 + 39x + 12x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(13 + 13x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(13 + 13x + 4x2)' equal to zero and attempt to solve: Simplifying 13 + 13x + 4x2 = 0 Solving 13 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.25 + 3.25x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + 3.25x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + 3.25x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + 3.25x + x2 = 0 + -3.25 3.25x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 3.25x + x2 = -3.25 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = -3.25 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = -3.25 + 2.640625 Combine like terms: -3.25 + 2.640625 = -0.609375 2.640625 + 3.25x + x2 = -0.609375 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = -0.609375 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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