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Simplifying 3X2 + -9X = 4 Reorder the terms: -9X + 3X2 = 4 Solving -9X + 3X2 = 4 Solving for variable 'X'. Reorder the terms: -4 + -9X + 3X2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + -9X + 3X2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -1.333333333 + -3X + X2 = 0 Move the constant term to the right: Add '1.333333333' to each side of the equation. -1.333333333 + -3X + 1.333333333 + X2 = 0 + 1.333333333 Reorder the terms: -1.333333333 + 1.333333333 + -3X + X2 = 0 + 1.333333333 Combine like terms: -1.333333333 + 1.333333333 = 0.000000000 0.000000000 + -3X + X2 = 0 + 1.333333333 -3X + X2 = 0 + 1.333333333 Combine like terms: 0 + 1.333333333 = 1.333333333 -3X + X2 = 1.333333333 The X term is -3X. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3X + 2.25 + X2 = 1.333333333 + 2.25 Reorder the terms: 2.25 + -3X + X2 = 1.333333333 + 2.25 Combine like terms: 1.333333333 + 2.25 = 3.583333333 2.25 + -3X + X2 = 3.583333333 Factor a perfect square on the left side: (X + -1.5)(X + -1.5) = 3.583333333 Calculate the square root of the right side: 1.892969449 Break this problem into two subproblems by setting (X + -1.5) equal to 1.892969449 and -1.892969449.Subproblem 1
X + -1.5 = 1.892969449 Simplifying X + -1.5 = 1.892969449 Reorder the terms: -1.5 + X = 1.892969449 Solving -1.5 + X = 1.892969449 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = 1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = 1.892969449 + 1.5 X = 1.892969449 + 1.5 Combine like terms: 1.892969449 + 1.5 = 3.392969449 X = 3.392969449 Simplifying X = 3.392969449Subproblem 2
X + -1.5 = -1.892969449 Simplifying X + -1.5 = -1.892969449 Reorder the terms: -1.5 + X = -1.892969449 Solving -1.5 + X = -1.892969449 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + X = -1.892969449 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + X = -1.892969449 + 1.5 X = -1.892969449 + 1.5 Combine like terms: -1.892969449 + 1.5 = -0.392969449 X = -0.392969449 Simplifying X = -0.392969449Solution
The solution to the problem is based on the solutions from the subproblems. X = {3.392969449, -0.392969449}
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