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Simplifying -11x2 + 3x + 13 = 0 Reorder the terms: 13 + 3x + -11x2 = 0 Solving 13 + 3x + -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 + -0.2727272727x + x2 = 0 Move the constant term to the right: Add '1.181818182' to each side of the equation. -1.181818182 + -0.2727272727x + 1.181818182 + x2 = 0 + 1.181818182 Reorder the terms: -1.181818182 + 1.181818182 + -0.2727272727x + x2 = 0 + 1.181818182 Combine like terms: -1.181818182 + 1.181818182 = 0.000000000 0.000000000 + -0.2727272727x + x2 = 0 + 1.181818182 -0.2727272727x + x2 = 0 + 1.181818182 Combine like terms: 0 + 1.181818182 = 1.181818182 -0.2727272727x + x2 = 1.181818182 The x term is -0.2727272727x. Take half its coefficient (-0.1363636364). Square it (0.01859504133) and add it to both sides. Add '0.01859504133' to each side of the equation. -0.2727272727x + 0.01859504133 + x2 = 1.181818182 + 0.01859504133 Reorder the terms: 0.01859504133 + -0.2727272727x + x2 = 1.181818182 + 0.01859504133 Combine like terms: 1.181818182 + 0.01859504133 = 1.20041322333 0.01859504133 + -0.2727272727x + x2 = 1.20041322333 Factor a perfect square on the left side: (x + -0.1363636364)(x + -0.1363636364) = 1.20041322333 Calculate the square root of the right side: 1.095633709 Break this problem into two subproblems by setting (x + -0.1363636364) equal to 1.095633709 and -1.095633709.Subproblem 1
x + -0.1363636364 = 1.095633709 Simplifying x + -0.1363636364 = 1.095633709 Reorder the terms: -0.1363636364 + x = 1.095633709 Solving -0.1363636364 + x = 1.095633709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + x = 1.095633709 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = 1.095633709 + 0.1363636364 x = 1.095633709 + 0.1363636364 Combine like terms: 1.095633709 + 0.1363636364 = 1.2319973454 x = 1.2319973454 Simplifying x = 1.2319973454Subproblem 2
x + -0.1363636364 = -1.095633709 Simplifying x + -0.1363636364 = -1.095633709 Reorder the terms: -0.1363636364 + x = -1.095633709 Solving -0.1363636364 + x = -1.095633709 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1363636364' to each side of the equation. -0.1363636364 + 0.1363636364 + x = -1.095633709 + 0.1363636364 Combine like terms: -0.1363636364 + 0.1363636364 = 0.0000000000 0.0000000000 + x = -1.095633709 + 0.1363636364 x = -1.095633709 + 0.1363636364 Combine like terms: -1.095633709 + 0.1363636364 = -0.9592700726 x = -0.9592700726 Simplifying x = -0.9592700726Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2319973454, -0.9592700726}
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