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Simplifying 0 = 3x2 + 10x + 11 Reorder the terms: 0 = 11 + 10x + 3x2 Solving 0 = 11 + 10x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -11 = -11 -11 + -10x + -3x2 = 11 + 10x + 3x2 + -11 + -10x + -3x2 Reorder the terms: -11 + -10x + -3x2 = 11 + -11 + 10x + -10x + 3x2 + -3x2 Combine like terms: 11 + -11 = 0 -11 + -10x + -3x2 = 0 + 10x + -10x + 3x2 + -3x2 -11 + -10x + -3x2 = 10x + -10x + 3x2 + -3x2 Combine like terms: 10x + -10x = 0 -11 + -10x + -3x2 = 0 + 3x2 + -3x2 -11 + -10x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -11 + -10x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(11 + 10x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(11 + 10x + 3x2)' equal to zero and attempt to solve: Simplifying 11 + 10x + 3x2 = 0 Solving 11 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.666666667 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-3.666666667' to each side of the equation. 3.666666667 + 3.333333333x + -3.666666667 + x2 = 0 + -3.666666667 Reorder the terms: 3.666666667 + -3.666666667 + 3.333333333x + x2 = 0 + -3.666666667 Combine like terms: 3.666666667 + -3.666666667 = 0.000000000 0.000000000 + 3.333333333x + x2 = 0 + -3.666666667 3.333333333x + x2 = 0 + -3.666666667 Combine like terms: 0 + -3.666666667 = -3.666666667 3.333333333x + x2 = -3.666666667 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = -3.666666667 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -3.666666667 + 2.777777779 Combine like terms: -3.666666667 + 2.777777779 = -0.888888888 2.777777779 + 3.333333333x + x2 = -0.888888888 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = -0.888888888 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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