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Simplifying 11x2 + -10x + -13 = 0 Reorder the terms: -13 + -10x + 11x2 = 0 Solving -13 + -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'. -1.181818182 + -0.9090909091x + x2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + -0.9090909091x + 1.181818182 + x2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + -0.9090909091x + x2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + -0.9090909091x + x2 = 0 + 1.181818182 -0.9090909091x + x2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 -0.9090909091x + x2 = 1.181818182 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 = 1.181818182 + 0.2066115703 Reorder the terms: 0.2066115703 + -0.9090909091x + x2 = 1.181818182 + 0.2066115703 Combine like terms: 1.181818182 + 0.2066115703 = 1.3884297523 0.2066115703 + -0.9090909091x + x2 = 1.3884297523 Factor a perfect square on the left side: (x + -0.4545454546)(x + -0.4545454546) = 1.3884297523 Calculate the square root of the right side: 1.178316491 Break this problem into two subproblems by setting (x + -0.4545454546) equal to 1.178316491 and -1.178316491.Subproblem 1
x + -0.4545454546 = 1.178316491 Simplifying x + -0.4545454546 = 1.178316491 Reorder the terms: -0.4545454546 + x = 1.178316491 Solving -0.4545454546 + x = 1.178316491 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 = 1.178316491 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = 1.178316491 + 0.4545454546 x = 1.178316491 + 0.4545454546 Combine like terms: 1.178316491 + 0.4545454546 = 1.6328619456 x = 1.6328619456 Simplifying x = 1.6328619456Subproblem 2
x + -0.4545454546 = -1.178316491 Simplifying x + -0.4545454546 = -1.178316491 Reorder the terms: -0.4545454546 + x = -1.178316491 Solving -0.4545454546 + x = -1.178316491 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 = -1.178316491 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = -1.178316491 + 0.4545454546 x = -1.178316491 + 0.4545454546 Combine like terms: -1.178316491 + 0.4545454546 = -0.7237710364 x = -0.7237710364 Simplifying x = -0.7237710364Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6328619456, -0.7237710364}
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