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Simplifying 0 = 3x2 + 10x + 9 Reorder the terms: 0 = 9 + 10x + 3x2 Solving 0 = 9 + 10x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -9 = -9 -9 + -10x + -3x2 = 9 + 10x + 3x2 + -9 + -10x + -3x2 Reorder the terms: -9 + -10x + -3x2 = 9 + -9 + 10x + -10x + 3x2 + -3x2 Combine like terms: 9 + -9 = 0 -9 + -10x + -3x2 = 0 + 10x + -10x + 3x2 + -3x2 -9 + -10x + -3x2 = 10x + -10x + 3x2 + -3x2 Combine like terms: 10x + -10x = 0 -9 + -10x + -3x2 = 0 + 3x2 + -3x2 -9 + -10x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -9 + -10x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 10x + 3x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 10x + 3x2)' equal to zero and attempt to solve: Simplifying 9 + 10x + 3x2 = 0 Solving 9 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + 3.333333333x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 3.333333333x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 3.333333333x + x2 = 0 + -3 3.333333333x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 3.333333333x + x2 = -3 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 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = -3 + 2.777777779 Combine like terms: -3 + 2.777777779 = -0.222222221 2.777777779 + 3.333333333x + x2 = -0.222222221 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = -0.222222221 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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