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Simplifying 11x2 + -65x + -36 = 0 Reorder the terms: -36 + -65x + 11x2 = 0 Solving -36 + -65x + 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'. -3.272727273 + -5.909090909x + x2 = 0 Move the constant term to the right: Add '3.272727273' to each side of the equation. -3.272727273 + -5.909090909x + 3.272727273 + x2 = 0 + 3.272727273 Reorder the terms: -3.272727273 + 3.272727273 + -5.909090909x + x2 = 0 + 3.272727273 Combine like terms: -3.272727273 + 3.272727273 = 0.000000000 0.000000000 + -5.909090909x + x2 = 0 + 3.272727273 -5.909090909x + x2 = 0 + 3.272727273 Combine like terms: 0 + 3.272727273 = 3.272727273 -5.909090909x + x2 = 3.272727273 The x term is -5.909090909x. Take half its coefficient (-2.954545455). Square it (8.729338846) and add it to both sides. Add '8.729338846' to each side of the equation. -5.909090909x + 8.729338846 + x2 = 3.272727273 + 8.729338846 Reorder the terms: 8.729338846 + -5.909090909x + x2 = 3.272727273 + 8.729338846 Combine like terms: 3.272727273 + 8.729338846 = 12.002066119 8.729338846 + -5.909090909x + x2 = 12.002066119 Factor a perfect square on the left side: (x + -2.954545455)(x + -2.954545455) = 12.002066119 Calculate the square root of the right side: 3.464399821 Break this problem into two subproblems by setting (x + -2.954545455) equal to 3.464399821 and -3.464399821.Subproblem 1
x + -2.954545455 = 3.464399821 Simplifying x + -2.954545455 = 3.464399821 Reorder the terms: -2.954545455 + x = 3.464399821 Solving -2.954545455 + x = 3.464399821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.954545455' to each side of the equation. -2.954545455 + 2.954545455 + x = 3.464399821 + 2.954545455 Combine like terms: -2.954545455 + 2.954545455 = 0.000000000 0.000000000 + x = 3.464399821 + 2.954545455 x = 3.464399821 + 2.954545455 Combine like terms: 3.464399821 + 2.954545455 = 6.418945276 x = 6.418945276 Simplifying x = 6.418945276Subproblem 2
x + -2.954545455 = -3.464399821 Simplifying x + -2.954545455 = -3.464399821 Reorder the terms: -2.954545455 + x = -3.464399821 Solving -2.954545455 + x = -3.464399821 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.954545455' to each side of the equation. -2.954545455 + 2.954545455 + x = -3.464399821 + 2.954545455 Combine like terms: -2.954545455 + 2.954545455 = 0.000000000 0.000000000 + x = -3.464399821 + 2.954545455 x = -3.464399821 + 2.954545455 Combine like terms: -3.464399821 + 2.954545455 = -0.509854366 x = -0.509854366 Simplifying x = -0.509854366Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.418945276, -0.509854366}
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