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Simplifying X + 1.732050808 + 3X2 + -9 = 0 Reorder the terms: 1.732050808 + -9 + X + 3X2 = 0 Combine like terms: 1.732050808 + -9 = -7.267949192 -7.267949192 + X + 3X2 = 0 Solving -7.267949192 + X + 3X2 = 0 Solving for variable 'X'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -2.422649731 + 0.3333333333X + X2 = 0 Move the constant term to the right: Add '2.422649731' to each side of the equation. -2.422649731 + 0.3333333333X + 2.422649731 + X2 = 0 + 2.422649731 Reorder the terms: -2.422649731 + 2.422649731 + 0.3333333333X + X2 = 0 + 2.422649731 Combine like terms: -2.422649731 + 2.422649731 = 0.000000000 0.000000000 + 0.3333333333X + X2 = 0 + 2.422649731 0.3333333333X + X2 = 0 + 2.422649731 Combine like terms: 0 + 2.422649731 = 2.422649731 0.3333333333X + X2 = 2.422649731 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. 0.3333333333X + 0.25 + X2 = 2.422649731 + 0.25 Reorder the terms: 0.25 + 0.3333333333X + X2 = 2.422649731 + 0.25 Combine like terms: 2.422649731 + 0.25 = 2.672649731 0.25 + 0.3333333333X + X2 = 2.672649731 Factor a perfect square on the left side: (X + 0.5)(X + 0.5) = 2.672649731 Calculate the square root of the right side: 1.634824067 Break this problem into two subproblems by setting (X + 0.5) equal to 1.634824067 and -1.634824067.Subproblem 1
X + 0.5 = 1.634824067 Simplifying X + 0.5 = 1.634824067 Reorder the terms: 0.5 + X = 1.634824067 Solving 0.5 + X = 1.634824067 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = 1.634824067 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = 1.634824067 + -0.5 X = 1.634824067 + -0.5 Combine like terms: 1.634824067 + -0.5 = 1.134824067 X = 1.134824067 Simplifying X = 1.134824067Subproblem 2
X + 0.5 = -1.634824067 Simplifying X + 0.5 = -1.634824067 Reorder the terms: 0.5 + X = -1.634824067 Solving 0.5 + X = -1.634824067 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + X = -1.634824067 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + X = -1.634824067 + -0.5 X = -1.634824067 + -0.5 Combine like terms: -1.634824067 + -0.5 = -2.134824067 X = -2.134824067 Simplifying X = -2.134824067Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.134824067, -2.134824067}
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