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Simplifying 3x(1 + -2x) + 2(3x + 7) = 29 (1 * 3x + -2x * 3x) + 2(3x + 7) = 29 (3x + -6x2) + 2(3x + 7) = 29 Reorder the terms: 3x + -6x2 + 2(7 + 3x) = 29 3x + -6x2 + (7 * 2 + 3x * 2) = 29 3x + -6x2 + (14 + 6x) = 29 Reorder the terms: 14 + 3x + 6x + -6x2 = 29 Combine like terms: 3x + 6x = 9x 14 + 9x + -6x2 = 29 Solving 14 + 9x + -6x2 = 29 Solving for variable 'x'. Reorder the terms: 14 + -29 + 9x + -6x2 = 29 + -29 Combine like terms: 14 + -29 = -15 -15 + 9x + -6x2 = 29 + -29 Combine like terms: 29 + -29 = 0 -15 + 9x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 3x + -2x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 3x + -2x2)' equal to zero and attempt to solve: Simplifying -5 + 3x + -2x2 = 0 Solving -5 + 3x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -1.5x + x2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -1.5x + -2.5 + x2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -1.5x + x2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -1.5x + x2 = 0 + -2.5 -1.5x + x2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -1.5x + x2 = -2.5 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = -2.5 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = -2.5 + 0.5625 Combine like terms: -2.5 + 0.5625 = -1.9375 0.5625 + -1.5x + x2 = -1.9375 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = -1.9375 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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