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Simplifying 3x2 + -1x + -60 = 0 Reorder the terms: -60 + -1x + 3x2 = 0 Solving -60 + -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'. -20 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -0.3333333333x + 20 + x2 = 0 + 20 Reorder the terms: -20 + 20 + -0.3333333333x + x2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -0.3333333333x + x2 = 0 + 20 -0.3333333333x + x2 = 0 + 20 Combine like terms: 0 + 20 = 20 -0.3333333333x + x2 = 20 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 = 20 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 20 + 0.02777777779 Combine like terms: 20 + 0.02777777779 = 20.02777777779 0.02777777779 + -0.3333333333x + x2 = 20.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 20.02777777779 Calculate the square root of the right side: 4.475240527 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 4.475240527 and -4.475240527.Subproblem 1
x + -0.1666666667 = 4.475240527 Simplifying x + -0.1666666667 = 4.475240527 Reorder the terms: -0.1666666667 + x = 4.475240527 Solving -0.1666666667 + x = 4.475240527 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 = 4.475240527 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 4.475240527 + 0.1666666667 x = 4.475240527 + 0.1666666667 Combine like terms: 4.475240527 + 0.1666666667 = 4.6419071937 x = 4.6419071937 Simplifying x = 4.6419071937Subproblem 2
x + -0.1666666667 = -4.475240527 Simplifying x + -0.1666666667 = -4.475240527 Reorder the terms: -0.1666666667 + x = -4.475240527 Solving -0.1666666667 + x = -4.475240527 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 = -4.475240527 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -4.475240527 + 0.1666666667 x = -4.475240527 + 0.1666666667 Combine like terms: -4.475240527 + 0.1666666667 = -4.3085738603 x = -4.3085738603 Simplifying x = -4.3085738603Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.6419071937, -4.3085738603}
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