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Simplifying -3x(2x + 1) + 3x = 6x + 3 Reorder the terms: -3x(1 + 2x) + 3x = 6x + 3 (1 * -3x + 2x * -3x) + 3x = 6x + 3 (-3x + -6x2) + 3x = 6x + 3 Reorder the terms: -3x + 3x + -6x2 = 6x + 3 Combine like terms: -3x + 3x = 0 0 + -6x2 = 6x + 3 -6x2 = 6x + 3 Reorder the terms: -6x2 = 3 + 6x Solving -6x2 = 3 + 6x Solving for variable 'x'. Reorder the terms: -3 + -6x + -6x2 = 3 + 6x + -3 + -6x Reorder the terms: -3 + -6x + -6x2 = 3 + -3 + 6x + -6x Combine like terms: 3 + -3 = 0 -3 + -6x + -6x2 = 0 + 6x + -6x -3 + -6x + -6x2 = 6x + -6x Combine like terms: 6x + -6x = 0 -3 + -6x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '-3'. -3(1 + 2x + 2x2) = 0 Ignore the factor -3.Subproblem 1
Set the factor '(1 + 2x + 2x2)' equal to zero and attempt to solve: Simplifying 1 + 2x + 2x2 = 0 Solving 1 + 2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.5 + x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x + x2 = 0 + -0.5 x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 x + x2 = -0.5 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. + 0.25 + x2 = -0.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 1.25 + x2 = -0.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.25 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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