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Simplifying 11x2 + -7x + -19 = 0 Reorder the terms: -19 + -7x + 11x2 = 0 Solving -19 + -7x + 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'. -1.727272727 + -0.6363636364x + x2 = 0 Move the constant term to the right: Add '1.727272727' to each side of the equation. -1.727272727 + -0.6363636364x + 1.727272727 + x2 = 0 + 1.727272727 Reorder the terms: -1.727272727 + 1.727272727 + -0.6363636364x + x2 = 0 + 1.727272727 Combine like terms: -1.727272727 + 1.727272727 = 0.000000000 0.000000000 + -0.6363636364x + x2 = 0 + 1.727272727 -0.6363636364x + x2 = 0 + 1.727272727 Combine like terms: 0 + 1.727272727 = 1.727272727 -0.6363636364x + x2 = 1.727272727 The x term is -0.6363636364x. Take half its coefficient (-0.3181818182). Square it (0.1012396694) and add it to both sides. Add '0.1012396694' to each side of the equation. -0.6363636364x + 0.1012396694 + x2 = 1.727272727 + 0.1012396694 Reorder the terms: 0.1012396694 + -0.6363636364x + x2 = 1.727272727 + 0.1012396694 Combine like terms: 1.727272727 + 0.1012396694 = 1.8285123964 0.1012396694 + -0.6363636364x + x2 = 1.8285123964 Factor a perfect square on the left side: (x + -0.3181818182)(x + -0.3181818182) = 1.8285123964 Calculate the square root of the right side: 1.35222498 Break this problem into two subproblems by setting (x + -0.3181818182) equal to 1.35222498 and -1.35222498.Subproblem 1
x + -0.3181818182 = 1.35222498 Simplifying x + -0.3181818182 = 1.35222498 Reorder the terms: -0.3181818182 + x = 1.35222498 Solving -0.3181818182 + x = 1.35222498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = 1.35222498 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = 1.35222498 + 0.3181818182 x = 1.35222498 + 0.3181818182 Combine like terms: 1.35222498 + 0.3181818182 = 1.6704067982 x = 1.6704067982 Simplifying x = 1.6704067982Subproblem 2
x + -0.3181818182 = -1.35222498 Simplifying x + -0.3181818182 = -1.35222498 Reorder the terms: -0.3181818182 + x = -1.35222498 Solving -0.3181818182 + x = -1.35222498 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3181818182' to each side of the equation. -0.3181818182 + 0.3181818182 + x = -1.35222498 + 0.3181818182 Combine like terms: -0.3181818182 + 0.3181818182 = 0.0000000000 0.0000000000 + x = -1.35222498 + 0.3181818182 x = -1.35222498 + 0.3181818182 Combine like terms: -1.35222498 + 0.3181818182 = -1.0340431618 x = -1.0340431618 Simplifying x = -1.0340431618Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.6704067982, -1.0340431618}
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