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Simplifying -2x(x + 2) + 3x = 12 Reorder the terms: -2x(2 + x) + 3x = 12 (2 * -2x + x * -2x) + 3x = 12 (-4x + -2x2) + 3x = 12 Reorder the terms: -4x + 3x + -2x2 = 12 Combine like terms: -4x + 3x = -1x -1x + -2x2 = 12 Solving -1x + -2x2 = 12 Solving for variable 'x'. Reorder the terms: -12 + -1x + -2x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -12 + -1x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(12 + x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(12 + x + 2x2)' equal to zero and attempt to solve: Simplifying 12 + x + 2x2 = 0 Solving 12 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 6 + 0.5x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + 0.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 0.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 0.5x + x2 = 0 + -6 0.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 0.5x + x2 = -6 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 = -6 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = -6 + 0.25 Combine like terms: -6 + 0.25 = -5.75 0.25 + 0.5x + x2 = -5.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -5.75 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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