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Simplifying 11x2 + 500x + 2500 = 0 Reorder the terms: 2500 + 500x + 11x2 = 0 Solving 2500 + 500x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 227.2727273 + 45.45454545x + x2 = 0 Move the constant term to the right: Add '-227.2727273' to each side of the equation. 227.2727273 + 45.45454545x + -227.2727273 + x2 = 0 + -227.2727273 Reorder the terms: 227.2727273 + -227.2727273 + 45.45454545x + x2 = 0 + -227.2727273 Combine like terms: 227.2727273 + -227.2727273 = 0.0000000 0.0000000 + 45.45454545x + x2 = 0 + -227.2727273 45.45454545x + x2 = 0 + -227.2727273 Combine like terms: 0 + -227.2727273 = -227.2727273 45.45454545x + x2 = -227.2727273 The x term is 45.45454545x. Take half its coefficient (22.72727273). Square it (516.5289257) and add it to both sides. Add '516.5289257' to each side of the equation. 45.45454545x + 516.5289257 + x2 = -227.2727273 + 516.5289257 Reorder the terms: 516.5289257 + 45.45454545x + x2 = -227.2727273 + 516.5289257 Combine like terms: -227.2727273 + 516.5289257 = 289.2561984 516.5289257 + 45.45454545x + x2 = 289.2561984 Factor a perfect square on the left side: (x + 22.72727273)(x + 22.72727273) = 289.2561984 Calculate the square root of the right side: 17.007533578 Break this problem into two subproblems by setting (x + 22.72727273) equal to 17.007533578 and -17.007533578.Subproblem 1
x + 22.72727273 = 17.007533578 Simplifying x + 22.72727273 = 17.007533578 Reorder the terms: 22.72727273 + x = 17.007533578 Solving 22.72727273 + x = 17.007533578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.72727273' to each side of the equation. 22.72727273 + -22.72727273 + x = 17.007533578 + -22.72727273 Combine like terms: 22.72727273 + -22.72727273 = 0.00000000 0.00000000 + x = 17.007533578 + -22.72727273 x = 17.007533578 + -22.72727273 Combine like terms: 17.007533578 + -22.72727273 = -5.719739152 x = -5.719739152 Simplifying x = -5.719739152Subproblem 2
x + 22.72727273 = -17.007533578 Simplifying x + 22.72727273 = -17.007533578 Reorder the terms: 22.72727273 + x = -17.007533578 Solving 22.72727273 + x = -17.007533578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-22.72727273' to each side of the equation. 22.72727273 + -22.72727273 + x = -17.007533578 + -22.72727273 Combine like terms: 22.72727273 + -22.72727273 = 0.00000000 0.00000000 + x = -17.007533578 + -22.72727273 x = -17.007533578 + -22.72727273 Combine like terms: -17.007533578 + -22.72727273 = -39.734806308 x = -39.734806308 Simplifying x = -39.734806308Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.719739152, -39.734806308}
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