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Simplifying 11x2 + 10x + -39 = 0 Reorder the terms: -39 + 10x + 11x2 = 0 Solving -39 + 10x + 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'. -3.545454545 + 0.9090909091x + x2 = 0 Move the constant term to the right: Add '3.545454545' to each side of the equation. -3.545454545 + 0.9090909091x + 3.545454545 + x2 = 0 + 3.545454545 Reorder the terms: -3.545454545 + 3.545454545 + 0.9090909091x + x2 = 0 + 3.545454545 Combine like terms: -3.545454545 + 3.545454545 = 0.000000000 0.000000000 + 0.9090909091x + x2 = 0 + 3.545454545 0.9090909091x + x2 = 0 + 3.545454545 Combine like terms: 0 + 3.545454545 = 3.545454545 0.9090909091x + x2 = 3.545454545 The x term is 0.9090909091x. Take half its coefficient (0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. 0.9090909091x + 0.2066115703 + x2 = 3.545454545 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091x + x2 = 3.545454545 + 0.2066115703 Combine like terms: 3.545454545 + 0.2066115703 = 3.7520661153 0.2066115703 + 0.9090909091x + x2 = 3.7520661153 Factor a perfect square on the left side: (x + 0.4545454546)(x + 0.4545454546) = 3.7520661153 Calculate the square root of the right side: 1.937025068 Break this problem into two subproblems by setting (x + 0.4545454546) equal to 1.937025068 and -1.937025068.Subproblem 1
x + 0.4545454546 = 1.937025068 Simplifying x + 0.4545454546 = 1.937025068 Reorder the terms: 0.4545454546 + x = 1.937025068 Solving 0.4545454546 + x = 1.937025068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + x = 1.937025068 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = 1.937025068 + -0.4545454546 x = 1.937025068 + -0.4545454546 Combine like terms: 1.937025068 + -0.4545454546 = 1.4824796134 x = 1.4824796134 Simplifying x = 1.4824796134Subproblem 2
x + 0.4545454546 = -1.937025068 Simplifying x + 0.4545454546 = -1.937025068 Reorder the terms: 0.4545454546 + x = -1.937025068 Solving 0.4545454546 + x = -1.937025068 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4545454546' to each side of the equation. 0.4545454546 + -0.4545454546 + x = -1.937025068 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = -1.937025068 + -0.4545454546 x = -1.937025068 + -0.4545454546 Combine like terms: -1.937025068 + -0.4545454546 = -2.3915705226 x = -2.3915705226 Simplifying x = -2.3915705226Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4824796134, -2.3915705226}
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