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Simplifying 11x2 + -21x + -34 = 0 Reorder the terms: -34 + -21x + 11x2 = 0 Solving -34 + -21x + 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'. -3.090909091 + -1.909090909x + x2 = 0 Move the constant term to the right: Add '3.090909091' to each side of the equation. -3.090909091 + -1.909090909x + 3.090909091 + x2 = 0 + 3.090909091 Reorder the terms: -3.090909091 + 3.090909091 + -1.909090909x + x2 = 0 + 3.090909091 Combine like terms: -3.090909091 + 3.090909091 = 0.000000000 0.000000000 + -1.909090909x + x2 = 0 + 3.090909091 -1.909090909x + x2 = 0 + 3.090909091 Combine like terms: 0 + 3.090909091 = 3.090909091 -1.909090909x + x2 = 3.090909091 The x term is -1.909090909x. Take half its coefficient (-0.9545454545). Square it (0.9111570247) and add it to both sides. Add '0.9111570247' to each side of the equation. -1.909090909x + 0.9111570247 + x2 = 3.090909091 + 0.9111570247 Reorder the terms: 0.9111570247 + -1.909090909x + x2 = 3.090909091 + 0.9111570247 Combine like terms: 3.090909091 + 0.9111570247 = 4.0020661157 0.9111570247 + -1.909090909x + x2 = 4.0020661157 Factor a perfect square on the left side: (x + -0.9545454545)(x + -0.9545454545) = 4.0020661157 Calculate the square root of the right side: 2.000516462 Break this problem into two subproblems by setting (x + -0.9545454545) equal to 2.000516462 and -2.000516462.Subproblem 1
x + -0.9545454545 = 2.000516462 Simplifying x + -0.9545454545 = 2.000516462 Reorder the terms: -0.9545454545 + x = 2.000516462 Solving -0.9545454545 + x = 2.000516462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + x = 2.000516462 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + x = 2.000516462 + 0.9545454545 x = 2.000516462 + 0.9545454545 Combine like terms: 2.000516462 + 0.9545454545 = 2.9550619165 x = 2.9550619165 Simplifying x = 2.9550619165Subproblem 2
x + -0.9545454545 = -2.000516462 Simplifying x + -0.9545454545 = -2.000516462 Reorder the terms: -0.9545454545 + x = -2.000516462 Solving -0.9545454545 + x = -2.000516462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9545454545' to each side of the equation. -0.9545454545 + 0.9545454545 + x = -2.000516462 + 0.9545454545 Combine like terms: -0.9545454545 + 0.9545454545 = 0.0000000000 0.0000000000 + x = -2.000516462 + 0.9545454545 x = -2.000516462 + 0.9545454545 Combine like terms: -2.000516462 + 0.9545454545 = -1.0459710075 x = -1.0459710075 Simplifying x = -1.0459710075Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.9550619165, -1.0459710075}
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