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Simplifying 2x2 + -3x + 2 = 252 Reorder the terms: 2 + -3x + 2x2 = 252 Solving 2 + -3x + 2x2 = 252 Solving for variable 'x'. Reorder the terms: 2 + -252 + -3x + 2x2 = 252 + -252 Combine like terms: 2 + -252 = -250 -250 + -3x + 2x2 = 252 + -252 Combine like terms: 252 + -252 = 0 -250 + -3x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -125 + -1.5x + x2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -1.5x + 125 + x2 = 0 + 125 Reorder the terms: -125 + 125 + -1.5x + x2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -1.5x + x2 = 0 + 125 -1.5x + x2 = 0 + 125 Combine like terms: 0 + 125 = 125 -1.5x + x2 = 125 The x term is -1.5x. Take half its coefficient (-0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. -1.5x + 0.5625 + x2 = 125 + 0.5625 Reorder the terms: 0.5625 + -1.5x + x2 = 125 + 0.5625 Combine like terms: 125 + 0.5625 = 125.5625 0.5625 + -1.5x + x2 = 125.5625 Factor a perfect square on the left side: (x + -0.75)(x + -0.75) = 125.5625 Calculate the square root of the right side: 11.205467416 Break this problem into two subproblems by setting (x + -0.75) equal to 11.205467416 and -11.205467416.Subproblem 1
x + -0.75 = 11.205467416 Simplifying x + -0.75 = 11.205467416 Reorder the terms: -0.75 + x = 11.205467416 Solving -0.75 + x = 11.205467416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = 11.205467416 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = 11.205467416 + 0.75 x = 11.205467416 + 0.75 Combine like terms: 11.205467416 + 0.75 = 11.955467416 x = 11.955467416 Simplifying x = 11.955467416Subproblem 2
x + -0.75 = -11.205467416 Simplifying x + -0.75 = -11.205467416 Reorder the terms: -0.75 + x = -11.205467416 Solving -0.75 + x = -11.205467416 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.75' to each side of the equation. -0.75 + 0.75 + x = -11.205467416 + 0.75 Combine like terms: -0.75 + 0.75 = 0.00 0.00 + x = -11.205467416 + 0.75 x = -11.205467416 + 0.75 Combine like terms: -11.205467416 + 0.75 = -10.455467416 x = -10.455467416 Simplifying x = -10.455467416Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.955467416, -10.455467416}
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