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Simplifying 11x2 + 10x + -5 = 0 Reorder the terms: -5 + 10x + 11x2 = 0 Solving -5 + 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'. -0.4545454545 + 0.9090909091x + x2 = 0 Move the constant term to the right: Add '0.4545454545' to each side of the equation. -0.4545454545 + 0.9090909091x + 0.4545454545 + x2 = 0 + 0.4545454545 Reorder the terms: -0.4545454545 + 0.4545454545 + 0.9090909091x + x2 = 0 + 0.4545454545 Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000 0.0000000000 + 0.9090909091x + x2 = 0 + 0.4545454545 0.9090909091x + x2 = 0 + 0.4545454545 Combine like terms: 0 + 0.4545454545 = 0.4545454545 0.9090909091x + x2 = 0.4545454545 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 = 0.4545454545 + 0.2066115703 Reorder the terms: 0.2066115703 + 0.9090909091x + x2 = 0.4545454545 + 0.2066115703 Combine like terms: 0.4545454545 + 0.2066115703 = 0.6611570248 0.2066115703 + 0.9090909091x + x2 = 0.6611570248 Factor a perfect square on the left side: (x + 0.4545454546)(x + 0.4545454546) = 0.6611570248 Calculate the square root of the right side: 0.813115628 Break this problem into two subproblems by setting (x + 0.4545454546) equal to 0.813115628 and -0.813115628.Subproblem 1
x + 0.4545454546 = 0.813115628 Simplifying x + 0.4545454546 = 0.813115628 Reorder the terms: 0.4545454546 + x = 0.813115628 Solving 0.4545454546 + x = 0.813115628 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 = 0.813115628 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = 0.813115628 + -0.4545454546 x = 0.813115628 + -0.4545454546 Combine like terms: 0.813115628 + -0.4545454546 = 0.3585701734 x = 0.3585701734 Simplifying x = 0.3585701734Subproblem 2
x + 0.4545454546 = -0.813115628 Simplifying x + 0.4545454546 = -0.813115628 Reorder the terms: 0.4545454546 + x = -0.813115628 Solving 0.4545454546 + x = -0.813115628 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 = -0.813115628 + -0.4545454546 Combine like terms: 0.4545454546 + -0.4545454546 = 0.0000000000 0.0000000000 + x = -0.813115628 + -0.4545454546 x = -0.813115628 + -0.4545454546 Combine like terms: -0.813115628 + -0.4545454546 = -1.2676610826 x = -1.2676610826 Simplifying x = -1.2676610826Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3585701734, -1.2676610826}
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