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Simplifying 6x2 + -23x + -3 = 0 Reorder the terms: -3 + -23x + 6x2 = 0 Solving -3 + -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'. -0.5 + -3.833333333x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -3.833333333x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -3.833333333x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -3.833333333x + x2 = 0 + 0.5 -3.833333333x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -3.833333333x + x2 = 0.5 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 = 0.5 + 3.673611112 Reorder the terms: 3.673611112 + -3.833333333x + x2 = 0.5 + 3.673611112 Combine like terms: 0.5 + 3.673611112 = 4.173611112 3.673611112 + -3.833333333x + x2 = 4.173611112 Factor a perfect square on the left side: (x + -1.916666667)(x + -1.916666667) = 4.173611112 Calculate the square root of the right side: 2.042941779 Break this problem into two subproblems by setting (x + -1.916666667) equal to 2.042941779 and -2.042941779.Subproblem 1
x + -1.916666667 = 2.042941779 Simplifying x + -1.916666667 = 2.042941779 Reorder the terms: -1.916666667 + x = 2.042941779 Solving -1.916666667 + x = 2.042941779 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 = 2.042941779 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = 2.042941779 + 1.916666667 x = 2.042941779 + 1.916666667 Combine like terms: 2.042941779 + 1.916666667 = 3.959608446 x = 3.959608446 Simplifying x = 3.959608446Subproblem 2
x + -1.916666667 = -2.042941779 Simplifying x + -1.916666667 = -2.042941779 Reorder the terms: -1.916666667 + x = -2.042941779 Solving -1.916666667 + x = -2.042941779 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 = -2.042941779 + 1.916666667 Combine like terms: -1.916666667 + 1.916666667 = 0.000000000 0.000000000 + x = -2.042941779 + 1.916666667 x = -2.042941779 + 1.916666667 Combine like terms: -2.042941779 + 1.916666667 = -0.126275112 x = -0.126275112 Simplifying x = -0.126275112Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.959608446, -0.126275112}
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