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Simplifying 11x2 + 8 + 30x = 0 Reorder the terms: 8 + 30x + 11x2 = 0 Solving 8 + 30x + 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'. 0.7272727273 + 2.727272727x + x2 = 0 Move the constant term to the right: Add '-0.7272727273' to each side of the equation. 0.7272727273 + 2.727272727x + -0.7272727273 + x2 = 0 + -0.7272727273 Reorder the terms: 0.7272727273 + -0.7272727273 + 2.727272727x + x2 = 0 + -0.7272727273 Combine like terms: 0.7272727273 + -0.7272727273 = 0.0000000000 0.0000000000 + 2.727272727x + x2 = 0 + -0.7272727273 2.727272727x + x2 = 0 + -0.7272727273 Combine like terms: 0 + -0.7272727273 = -0.7272727273 2.727272727x + x2 = -0.7272727273 The x term is 2.727272727x. Take half its coefficient (1.363636364). Square it (1.859504133) and add it to both sides. Add '1.859504133' to each side of the equation. 2.727272727x + 1.859504133 + x2 = -0.7272727273 + 1.859504133 Reorder the terms: 1.859504133 + 2.727272727x + x2 = -0.7272727273 + 1.859504133 Combine like terms: -0.7272727273 + 1.859504133 = 1.1322314057 1.859504133 + 2.727272727x + x2 = 1.1322314057 Factor a perfect square on the left side: (x + 1.363636364)(x + 1.363636364) = 1.1322314057 Calculate the square root of the right side: 1.064063629 Break this problem into two subproblems by setting (x + 1.363636364) equal to 1.064063629 and -1.064063629.Subproblem 1
x + 1.363636364 = 1.064063629 Simplifying x + 1.363636364 = 1.064063629 Reorder the terms: 1.363636364 + x = 1.064063629 Solving 1.363636364 + x = 1.064063629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = 1.064063629 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = 1.064063629 + -1.363636364 x = 1.064063629 + -1.363636364 Combine like terms: 1.064063629 + -1.363636364 = -0.299572735 x = -0.299572735 Simplifying x = -0.299572735Subproblem 2
x + 1.363636364 = -1.064063629 Simplifying x + 1.363636364 = -1.064063629 Reorder the terms: 1.363636364 + x = -1.064063629 Solving 1.363636364 + x = -1.064063629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.363636364' to each side of the equation. 1.363636364 + -1.363636364 + x = -1.064063629 + -1.363636364 Combine like terms: 1.363636364 + -1.363636364 = 0.000000000 0.000000000 + x = -1.064063629 + -1.363636364 x = -1.064063629 + -1.363636364 Combine like terms: -1.064063629 + -1.363636364 = -2.427699993 x = -2.427699993 Simplifying x = -2.427699993Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.299572735, -2.427699993}
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