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Simplifying 30x = 9x2 + 36 Reorder the terms: 30x = 36 + 9x2 Solving 30x = 36 + 9x2 Solving for variable 'x'. Reorder the terms: -36 + 30x + -9x2 = 36 + 9x2 + -36 + -9x2 Reorder the terms: -36 + 30x + -9x2 = 36 + -36 + 9x2 + -9x2 Combine like terms: 36 + -36 = 0 -36 + 30x + -9x2 = 0 + 9x2 + -9x2 -36 + 30x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 -36 + 30x + -9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + 10x + -3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-12 + 10x + -3x2)' equal to zero and attempt to solve: Simplifying -12 + 10x + -3x2 = 0 Solving -12 + 10x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 4 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '-4' to each side of the equation. 4 + -3.333333333x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + -3.333333333x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3.333333333x + x2 = 0 + -4 -3.333333333x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 -3.333333333x + x2 = -4 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 = -4 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = -4 + 2.777777779 Combine like terms: -4 + 2.777777779 = -1.222222221 2.777777779 + -3.333333333x + x2 = -1.222222221 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = -1.222222221 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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