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Simplifying 11x2 + 6x + -9 = 0 Reorder the terms: -9 + 6x + 11x2 = 0 Solving -9 + 6x + 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'. -0.8181818182 + 0.5454545455x + x2 = 0 Move the constant term to the right: Add '0.8181818182' to each side of the equation. -0.8181818182 + 0.5454545455x + 0.8181818182 + x2 = 0 + 0.8181818182 Reorder the terms: -0.8181818182 + 0.8181818182 + 0.5454545455x + x2 = 0 + 0.8181818182 Combine like terms: -0.8181818182 + 0.8181818182 = 0.0000000000 0.0000000000 + 0.5454545455x + x2 = 0 + 0.8181818182 0.5454545455x + x2 = 0 + 0.8181818182 Combine like terms: 0 + 0.8181818182 = 0.8181818182 0.5454545455x + x2 = 0.8181818182 The x term is 0.5454545455x. Take half its coefficient (0.2727272728). Square it (0.07438016533) and add it to both sides. Add '0.07438016533' to each side of the equation. 0.5454545455x + 0.07438016533 + x2 = 0.8181818182 + 0.07438016533 Reorder the terms: 0.07438016533 + 0.5454545455x + x2 = 0.8181818182 + 0.07438016533 Combine like terms: 0.8181818182 + 0.07438016533 = 0.89256198353 0.07438016533 + 0.5454545455x + x2 = 0.89256198353 Factor a perfect square on the left side: (x + 0.2727272728)(x + 0.2727272728) = 0.89256198353 Calculate the square root of the right side: 0.944754986 Break this problem into two subproblems by setting (x + 0.2727272728) equal to 0.944754986 and -0.944754986.Subproblem 1
x + 0.2727272728 = 0.944754986 Simplifying x + 0.2727272728 = 0.944754986 Reorder the terms: 0.2727272728 + x = 0.944754986 Solving 0.2727272728 + x = 0.944754986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = 0.944754986 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = 0.944754986 + -0.2727272728 x = 0.944754986 + -0.2727272728 Combine like terms: 0.944754986 + -0.2727272728 = 0.6720277132 x = 0.6720277132 Simplifying x = 0.6720277132Subproblem 2
x + 0.2727272728 = -0.944754986 Simplifying x + 0.2727272728 = -0.944754986 Reorder the terms: 0.2727272728 + x = -0.944754986 Solving 0.2727272728 + x = -0.944754986 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2727272728' to each side of the equation. 0.2727272728 + -0.2727272728 + x = -0.944754986 + -0.2727272728 Combine like terms: 0.2727272728 + -0.2727272728 = 0.0000000000 0.0000000000 + x = -0.944754986 + -0.2727272728 x = -0.944754986 + -0.2727272728 Combine like terms: -0.944754986 + -0.2727272728 = -1.2174822588 x = -1.2174822588 Simplifying x = -1.2174822588Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6720277132, -1.2174822588}
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