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Simplifying 2x2 + 5x + -333 = 0 Reorder the terms: -333 + 5x + 2x2 = 0 Solving -333 + 5x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -166.5 + 2.5x + x2 = 0 Move the constant term to the right: Add '166.5' to each side of the equation. -166.5 + 2.5x + 166.5 + x2 = 0 + 166.5 Reorder the terms: -166.5 + 166.5 + 2.5x + x2 = 0 + 166.5 Combine like terms: -166.5 + 166.5 = 0.0 0.0 + 2.5x + x2 = 0 + 166.5 2.5x + x2 = 0 + 166.5 Combine like terms: 0 + 166.5 = 166.5 2.5x + x2 = 166.5 The x term is 2.5x. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5x + 1.5625 + x2 = 166.5 + 1.5625 Reorder the terms: 1.5625 + 2.5x + x2 = 166.5 + 1.5625 Combine like terms: 166.5 + 1.5625 = 168.0625 1.5625 + 2.5x + x2 = 168.0625 Factor a perfect square on the left side: (x + 1.25)(x + 1.25) = 168.0625 Calculate the square root of the right side: 12.963892162 Break this problem into two subproblems by setting (x + 1.25) equal to 12.963892162 and -12.963892162.Subproblem 1
x + 1.25 = 12.963892162 Simplifying x + 1.25 = 12.963892162 Reorder the terms: 1.25 + x = 12.963892162 Solving 1.25 + x = 12.963892162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 12.963892162 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 12.963892162 + -1.25 x = 12.963892162 + -1.25 Combine like terms: 12.963892162 + -1.25 = 11.713892162 x = 11.713892162 Simplifying x = 11.713892162Subproblem 2
x + 1.25 = -12.963892162 Simplifying x + 1.25 = -12.963892162 Reorder the terms: 1.25 + x = -12.963892162 Solving 1.25 + x = -12.963892162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -12.963892162 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -12.963892162 + -1.25 x = -12.963892162 + -1.25 Combine like terms: -12.963892162 + -1.25 = -14.213892162 x = -14.213892162 Simplifying x = -14.213892162Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.713892162, -14.213892162}
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