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Simplifying 0 = 20 + 30x + 30x2 Solving 0 = 20 + 30x + 30x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -30x + -30x2 = 20 + 30x + 30x2 + -20 + -30x + -30x2 Reorder the terms: -20 + -30x + -30x2 = 20 + -20 + 30x + -30x + 30x2 + -30x2 Combine like terms: 20 + -20 = 0 -20 + -30x + -30x2 = 0 + 30x + -30x + 30x2 + -30x2 -20 + -30x + -30x2 = 30x + -30x + 30x2 + -30x2 Combine like terms: 30x + -30x = 0 -20 + -30x + -30x2 = 0 + 30x2 + -30x2 -20 + -30x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 -20 + -30x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '-10'. -10(2 + 3x + 3x2) = 0 Ignore the factor -10.Subproblem 1
Set the factor '(2 + 3x + 3x2)' equal to zero and attempt to solve: Simplifying 2 + 3x + 3x2 = 0 Solving 2 + 3x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + x + x2 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + x + -0.6666666667 + x2 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + x + x2 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + x + x2 = 0 + -0.6666666667 x + x2 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 x + x2 = -0.6666666667 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 = -0.6666666667 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = -0.6666666667 + 0.25 Combine like terms: -0.6666666667 + 0.25 = -0.4166666667 1.25 + x2 = -0.4166666667 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.4166666667 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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