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Simplifying 0 = 2x2 + -9x + 3 Reorder the terms: 0 = 3 + -9x + 2x2 Solving 0 = 3 + -9x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + 9x + -2x2 = 3 + -9x + 2x2 + -3 + 9x + -2x2 Reorder the terms: -3 + 9x + -2x2 = 3 + -3 + -9x + 9x + 2x2 + -2x2 Combine like terms: 3 + -3 = 0 -3 + 9x + -2x2 = 0 + -9x + 9x + 2x2 + -2x2 -3 + 9x + -2x2 = -9x + 9x + 2x2 + -2x2 Combine like terms: -9x + 9x = 0 -3 + 9x + -2x2 = 0 + 2x2 + -2x2 -3 + 9x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -3 + 9x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 1.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '-1.5' to each side of the equation. 1.5 + -4.5x + -1.5 + x2 = 0 + -1.5 Reorder the terms: 1.5 + -1.5 + -4.5x + x2 = 0 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + -4.5x + x2 = 0 + -1.5 -4.5x + x2 = 0 + -1.5 Combine like terms: 0 + -1.5 = -1.5 -4.5x + x2 = -1.5 The x term is -4.5x. Take half its coefficient (-2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. -4.5x + 5.0625 + x2 = -1.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = -1.5 + 5.0625 Combine like terms: -1.5 + 5.0625 = 3.5625 5.0625 + -4.5x + x2 = 3.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 3.5625 Calculate the square root of the right side: 1.887458609 Break this problem into two subproblems by setting (x + -2.25) equal to 1.887458609 and -1.887458609.Subproblem 1
x + -2.25 = 1.887458609 Simplifying x + -2.25 = 1.887458609 Reorder the terms: -2.25 + x = 1.887458609 Solving -2.25 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = 1.887458609 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 1.887458609 + 2.25 x = 1.887458609 + 2.25 Combine like terms: 1.887458609 + 2.25 = 4.137458609 x = 4.137458609 Simplifying x = 4.137458609Subproblem 2
x + -2.25 = -1.887458609 Simplifying x + -2.25 = -1.887458609 Reorder the terms: -2.25 + x = -1.887458609 Solving -2.25 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + x = -1.887458609 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -1.887458609 + 2.25 x = -1.887458609 + 2.25 Combine like terms: -1.887458609 + 2.25 = 0.362541391 x = 0.362541391 Simplifying x = 0.362541391Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.137458609, 0.362541391}
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