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Simplifying 6x2 + -23x + -6 = 0 Reorder the terms: -6 + -23x + 6x2 = 0 Solving -6 + -23x + 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 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + -3.833333333x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -3.833333333x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3.833333333x + x2 = 0 + 1 -3.833333333x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3.833333333x + x2 = 1 The x term is -3.833333333x. Take half its coefficient (-1.916666667). Square it (3.673611112) and add it to both sides. Add '3.673611112' to each side of the equation. -3.833333333x + 3.673611112 + x2 = 1 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = 1 + 3.673611112 Combine like terms: 1 + 3.673611112 = 4.673611112 3.673611112 + -3.833333333x + x2 = 4.673611112 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 4.673611112 Calculate the square root of the right side: 2.161853629 Break this problem into two subproblems by setting (x + -1.916666667) equal to 2.161853629 and -2.161853629.Subproblem 1
x + -1.916666667 = 2.161853629 Simplifying x + -1.916666667 = 2.161853629 Reorder the terms: -1.916666667 + x = 2.161853629 Solving -1.916666667 + x = 2.161853629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = 2.161853629 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 2.161853629 + 1.916666667 x = 2.161853629 + 1.916666667 Combine like terms: 2.161853629 + 1.916666667 = 4.078520296 x = 4.078520296 Simplifying x = 4.078520296Subproblem 2
x + -1.916666667 = -2.161853629 Simplifying x + -1.916666667 = -2.161853629 Reorder the terms: -1.916666667 + x = -2.161853629 Solving -1.916666667 + x = -2.161853629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.916666667' to each side of the equation. -1.916666667 + 1.916666667 + x = -2.161853629 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -2.161853629 + 1.916666667 x = -2.161853629 + 1.916666667 Combine like terms: -2.161853629 + 1.916666667 = -0.245186962 x = -0.245186962 Simplifying x = -0.245186962Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.078520296, -0.245186962}
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