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Simplifying 11x2 + 50x + -1 = 0 Reorder the terms: -1 + 50x + 11x2 = 0 Solving -1 + 50x + 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'. -0.09090909091 + 4.545454545x + x2 = 0 Move the constant term to the right: Add '0.09090909091' to each side of the equation. -0.09090909091 + 4.545454545x + 0.09090909091 + x2 = 0 + 0.09090909091 Reorder the terms: -0.09090909091 + 0.09090909091 + 4.545454545x + x2 = 0 + 0.09090909091 Combine like terms: -0.09090909091 + 0.09090909091 = 0.00000000000 0.00000000000 + 4.545454545x + x2 = 0 + 0.09090909091 4.545454545x + x2 = 0 + 0.09090909091 Combine like terms: 0 + 0.09090909091 = 0.09090909091 4.545454545x + x2 = 0.09090909091 The x term is 4.545454545x. Take half its coefficient (2.272727273). Square it (5.165289257) and add it to both sides. Add '5.165289257' to each side of the equation. 4.545454545x + 5.165289257 + x2 = 0.09090909091 + 5.165289257 Reorder the terms: 5.165289257 + 4.545454545x + x2 = 0.09090909091 + 5.165289257 Combine like terms: 0.09090909091 + 5.165289257 = 5.25619834791 5.165289257 + 4.545454545x + x2 = 5.25619834791 Factor a perfect square on the left side: (x + 2.272727273)(x + 2.272727273) = 5.25619834791 Calculate the square root of the right side: 2.292640039 Break this problem into two subproblems by setting (x + 2.272727273) equal to 2.292640039 and -2.292640039.Subproblem 1
x + 2.272727273 = 2.292640039 Simplifying x + 2.272727273 = 2.292640039 Reorder the terms: 2.272727273 + x = 2.292640039 Solving 2.272727273 + x = 2.292640039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.272727273' to each side of the equation. 2.272727273 + -2.272727273 + x = 2.292640039 + -2.272727273 Combine like terms: 2.272727273 + -2.272727273 = 0.000000000 0.000000000 + x = 2.292640039 + -2.272727273 x = 2.292640039 + -2.272727273 Combine like terms: 2.292640039 + -2.272727273 = 0.019912766 x = 0.019912766 Simplifying x = 0.019912766Subproblem 2
x + 2.272727273 = -2.292640039 Simplifying x + 2.272727273 = -2.292640039 Reorder the terms: 2.272727273 + x = -2.292640039 Solving 2.272727273 + x = -2.292640039 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.272727273' to each side of the equation. 2.272727273 + -2.272727273 + x = -2.292640039 + -2.272727273 Combine like terms: 2.272727273 + -2.272727273 = 0.000000000 0.000000000 + x = -2.292640039 + -2.272727273 x = -2.292640039 + -2.272727273 Combine like terms: -2.292640039 + -2.272727273 = -4.565367312 x = -4.565367312 Simplifying x = -4.565367312Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.019912766, -4.565367312}
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