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Simplifying -3x2 + 6x + 392 = 0 Reorder the terms: 392 + 6x + -3x2 = 0 Solving 392 + 6x + -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'. -130.6666667 + -2x + x2 = 0 Move the constant term to the right: Add '130.6666667' to each side of the equation. -130.6666667 + -2x + 130.6666667 + x2 = 0 + 130.6666667 Reorder the terms: -130.6666667 + 130.6666667 + -2x + x2 = 0 + 130.6666667 Combine like terms: -130.6666667 + 130.6666667 = 0.0000000 0.0000000 + -2x + x2 = 0 + 130.6666667 -2x + x2 = 0 + 130.6666667 Combine like terms: 0 + 130.6666667 = 130.6666667 -2x + x2 = 130.6666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 130.6666667 + 1 Reorder the terms: 1 + -2x + x2 = 130.6666667 + 1 Combine like terms: 130.6666667 + 1 = 131.6666667 1 + -2x + x2 = 131.6666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 131.6666667 Calculate the square root of the right side: 11.474609653 Break this problem into two subproblems by setting (x + -1) equal to 11.474609653 and -11.474609653.Subproblem 1
x + -1 = 11.474609653 Simplifying x + -1 = 11.474609653 Reorder the terms: -1 + x = 11.474609653 Solving -1 + x = 11.474609653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 11.474609653 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.474609653 + 1 x = 11.474609653 + 1 Combine like terms: 11.474609653 + 1 = 12.474609653 x = 12.474609653 Simplifying x = 12.474609653Subproblem 2
x + -1 = -11.474609653 Simplifying x + -1 = -11.474609653 Reorder the terms: -1 + x = -11.474609653 Solving -1 + x = -11.474609653 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -11.474609653 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.474609653 + 1 x = -11.474609653 + 1 Combine like terms: -11.474609653 + 1 = -10.474609653 x = -10.474609653 Simplifying x = -10.474609653Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.474609653, -10.474609653}
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