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Simplifying 3x2 + 12x + -1040 = 0 Reorder the terms: -1040 + 12x + 3x2 = 0 Solving -1040 + 12x + 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'. -346.6666667 + 4x + x2 = 0 Move the constant term to the right: Add '346.6666667' to each side of the equation. -346.6666667 + 4x + 346.6666667 + x2 = 0 + 346.6666667 Reorder the terms: -346.6666667 + 346.6666667 + 4x + x2 = 0 + 346.6666667 Combine like terms: -346.6666667 + 346.6666667 = 0.0000000 0.0000000 + 4x + x2 = 0 + 346.6666667 4x + x2 = 0 + 346.6666667 Combine like terms: 0 + 346.6666667 = 346.6666667 4x + x2 = 346.6666667 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 346.6666667 + 4 Reorder the terms: 4 + 4x + x2 = 346.6666667 + 4 Combine like terms: 346.6666667 + 4 = 350.6666667 4 + 4x + x2 = 350.6666667 Factor a perfect square on the left side: (x + 2)(x + 2) = 350.6666667 Calculate the square root of the right side: 18.726095874 Break this problem into two subproblems by setting (x + 2) equal to 18.726095874 and -18.726095874.Subproblem 1
x + 2 = 18.726095874 Simplifying x + 2 = 18.726095874 Reorder the terms: 2 + x = 18.726095874 Solving 2 + x = 18.726095874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 18.726095874 + -2 Combine like terms: 2 + -2 = 0 0 + x = 18.726095874 + -2 x = 18.726095874 + -2 Combine like terms: 18.726095874 + -2 = 16.726095874 x = 16.726095874 Simplifying x = 16.726095874Subproblem 2
x + 2 = -18.726095874 Simplifying x + 2 = -18.726095874 Reorder the terms: 2 + x = -18.726095874 Solving 2 + x = -18.726095874 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -18.726095874 + -2 Combine like terms: 2 + -2 = 0 0 + x = -18.726095874 + -2 x = -18.726095874 + -2 Combine like terms: -18.726095874 + -2 = -20.726095874 x = -20.726095874 Simplifying x = -20.726095874Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.726095874, -20.726095874}
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