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Simplifying 6x2 + -13x + -11 = 0 Reorder the terms: -11 + -13x + 6x2 = 0 Solving -11 + -13x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -1.833333333 + -2.166666667x + x2 = 0 Move the constant term to the right: Add '1.833333333' to each side of the equation. -1.833333333 + -2.166666667x + 1.833333333 + x2 = 0 + 1.833333333 Reorder the terms: -1.833333333 + 1.833333333 + -2.166666667x + x2 = 0 + 1.833333333 Combine like terms: -1.833333333 + 1.833333333 = 0.000000000 0.000000000 + -2.166666667x + x2 = 0 + 1.833333333 -2.166666667x + x2 = 0 + 1.833333333 Combine like terms: 0 + 1.833333333 = 1.833333333 -2.166666667x + x2 = 1.833333333 The x term is -2.166666667x. Take half its coefficient (-1.083333334). Square it (1.173611113) and add it to both sides. Add '1.173611113' to each side of the equation. -2.166666667x + 1.173611113 + x2 = 1.833333333 + 1.173611113 Reorder the terms: 1.173611113 + -2.166666667x + x2 = 1.833333333 + 1.173611113 Combine like terms: 1.833333333 + 1.173611113 = 3.006944446 1.173611113 + -2.166666667x + x2 = 3.006944446 Factor a perfect square on the left side: (x + -1.083333334)(x + -1.083333334) = 3.006944446 Calculate the square root of the right side: 1.734054338 Break this problem into two subproblems by setting (x + -1.083333334) equal to 1.734054338 and -1.734054338.Subproblem 1
x + -1.083333334 = 1.734054338 Simplifying x + -1.083333334 = 1.734054338 Reorder the terms: -1.083333334 + x = 1.734054338 Solving -1.083333334 + x = 1.734054338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = 1.734054338 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = 1.734054338 + 1.083333334 x = 1.734054338 + 1.083333334 Combine like terms: 1.734054338 + 1.083333334 = 2.817387672 x = 2.817387672 Simplifying x = 2.817387672Subproblem 2
x + -1.083333334 = -1.734054338 Simplifying x + -1.083333334 = -1.734054338 Reorder the terms: -1.083333334 + x = -1.734054338 Solving -1.083333334 + x = -1.734054338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.083333334' to each side of the equation. -1.083333334 + 1.083333334 + x = -1.734054338 + 1.083333334 Combine like terms: -1.083333334 + 1.083333334 = 0.000000000 0.000000000 + x = -1.734054338 + 1.083333334 x = -1.734054338 + 1.083333334 Combine like terms: -1.734054338 + 1.083333334 = -0.650721004 x = -0.650721004 Simplifying x = -0.650721004Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.817387672, -0.650721004}
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