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Simplifying 0 = 2x2 + 6x + 11 Reorder the terms: 0 = 11 + 6x + 2x2 Solving 0 = 11 + 6x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -6x + -2x2 = 11 + 6x + 2x2 + -11 + -6x + -2x2 Reorder the terms: -11 + -6x + -2x2 = 11 + -11 + 6x + -6x + 2x2 + -2x2 Combine like terms: 11 + -11 = 0 -11 + -6x + -2x2 = 0 + 6x + -6x + 2x2 + -2x2 -11 + -6x + -2x2 = 6x + -6x + 2x2 + -2x2 Combine like terms: 6x + -6x = 0 -11 + -6x + -2x2 = 0 + 2x2 + -2x2 -11 + -6x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -11 + -6x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 6x + 2x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 6x + 2x2)' equal to zero and attempt to solve: Simplifying 11 + 6x + 2x2 = 0 Solving 11 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 5.5 + 3x + x2 = 0 Move the constant term to the right: Add '-5.5' to each side of the equation. 5.5 + 3x + -5.5 + x2 = 0 + -5.5 Reorder the terms: 5.5 + -5.5 + 3x + x2 = 0 + -5.5 Combine like terms: 5.5 + -5.5 = 0.0 0.0 + 3x + x2 = 0 + -5.5 3x + x2 = 0 + -5.5 Combine like terms: 0 + -5.5 = -5.5 3x + x2 = -5.5 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = -5.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = -5.5 + 2.25 Combine like terms: -5.5 + 2.25 = -3.25 2.25 + 3x + x2 = -3.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = -3.25 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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