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Simplifying 11x2 + -28x + -28 = 0 Reorder the terms: -28 + -28x + 11x2 = 0 Solving -28 + -28x + 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'. -2.545454545 + -2.545454545x + x2 = 0 Move the constant term to the right: Add '2.545454545' to each side of the equation. -2.545454545 + -2.545454545x + 2.545454545 + x2 = 0 + 2.545454545 Reorder the terms: -2.545454545 + 2.545454545 + -2.545454545x + x2 = 0 + 2.545454545 Combine like terms: -2.545454545 + 2.545454545 = 0.000000000 0.000000000 + -2.545454545x + x2 = 0 + 2.545454545 -2.545454545x + x2 = 0 + 2.545454545 Combine like terms: 0 + 2.545454545 = 2.545454545 -2.545454545x + x2 = 2.545454545 The x term is -2.545454545x. Take half its coefficient (-1.272727273). Square it (1.619834711) and add it to both sides. Add '1.619834711' to each side of the equation. -2.545454545x + 1.619834711 + x2 = 2.545454545 + 1.619834711 Reorder the terms: 1.619834711 + -2.545454545x + x2 = 2.545454545 + 1.619834711 Combine like terms: 2.545454545 + 1.619834711 = 4.165289256 1.619834711 + -2.545454545x + x2 = 4.165289256 Factor a perfect square on the left side: (x + -1.272727273)(x + -1.272727273) = 4.165289256 Calculate the square root of the right side: 2.040904029 Break this problem into two subproblems by setting (x + -1.272727273) equal to 2.040904029 and -2.040904029.Subproblem 1
x + -1.272727273 = 2.040904029 Simplifying x + -1.272727273 = 2.040904029 Reorder the terms: -1.272727273 + x = 2.040904029 Solving -1.272727273 + x = 2.040904029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = 2.040904029 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = 2.040904029 + 1.272727273 x = 2.040904029 + 1.272727273 Combine like terms: 2.040904029 + 1.272727273 = 3.313631302 x = 3.313631302 Simplifying x = 3.313631302Subproblem 2
x + -1.272727273 = -2.040904029 Simplifying x + -1.272727273 = -2.040904029 Reorder the terms: -1.272727273 + x = -2.040904029 Solving -1.272727273 + x = -2.040904029 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = -2.040904029 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = -2.040904029 + 1.272727273 x = -2.040904029 + 1.272727273 Combine like terms: -2.040904029 + 1.272727273 = -0.768176756 x = -0.768176756 Simplifying x = -0.768176756Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.313631302, -0.768176756}
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