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Simplifying 2x[2x + 1] = -12 Reorder the terms: 2x[1 + 2x] = -12 [1 * 2x + 2x * 2x] = -12 [2x + 4x2] = -12 Solving 2x + 4x2 = -12 Solving for variable 'x'. Reorder the terms: 12 + 2x + 4x2 = -12 + 12 Combine like terms: -12 + 12 = 0 12 + 2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(6 + x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(6 + x + 2x2)' equal to zero and attempt to solve: Simplifying 6 + x + 2x2 = 0 Solving 6 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 3 + 0.5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 0.5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 0.5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 0.5x + x2 = 0 + -3 0.5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 0.5x + x2 = -3 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. 0.5x + 0.25 + x2 = -3 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -3 + 0.25 Combine like terms: -3 + 0.25 = -2.75 0.25 + 0.5x + x2 = -2.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -2.75 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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