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Simplifying 3x2 + -1x + -51 = 0 Reorder the terms: -51 + -1x + 3x2 = 0 Solving -51 + -1x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -17 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '17' to each side of the equation. -17 + -0.3333333333x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + -0.3333333333x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -0.3333333333x + x2 = 0 + 17 -0.3333333333x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 -0.3333333333x + x2 = 17 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 17 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 17 + 0.02777777779 Combine like terms: 17 + 0.02777777779 = 17.02777777779 0.02777777779 + -0.3333333333x + x2 = 17.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 17.02777777779 Calculate the square root of the right side: 4.126472801 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 4.126472801 and -4.126472801.Subproblem 1
x + -0.1666666667 = 4.126472801 Simplifying x + -0.1666666667 = 4.126472801 Reorder the terms: -0.1666666667 + x = 4.126472801 Solving -0.1666666667 + x = 4.126472801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 4.126472801 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 4.126472801 + 0.1666666667 x = 4.126472801 + 0.1666666667 Combine like terms: 4.126472801 + 0.1666666667 = 4.2931394677 x = 4.2931394677 Simplifying x = 4.2931394677Subproblem 2
x + -0.1666666667 = -4.126472801 Simplifying x + -0.1666666667 = -4.126472801 Reorder the terms: -0.1666666667 + x = -4.126472801 Solving -0.1666666667 + x = -4.126472801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -4.126472801 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -4.126472801 + 0.1666666667 x = -4.126472801 + 0.1666666667 Combine like terms: -4.126472801 + 0.1666666667 = -3.9598061343 x = -3.9598061343 Simplifying x = -3.9598061343Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2931394677, -3.9598061343}
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