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Simplifying 340 = x(3x + -6) Reorder the terms: 340 = x(-6 + 3x) 340 = (-6 * x + 3x * x) 340 = (-6x + 3x2) Solving 340 = -6x + 3x2 Solving for variable 'x'. Reorder the terms: 340 + 6x + -3x2 = -6x + 6x + 3x2 + -3x2 Combine like terms: -6x + 6x = 0 340 + 6x + -3x2 = 0 + 3x2 + -3x2 340 + 6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 340 + 6x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -113.3333333 + -2x + x2 = 0 Move the constant term to the right: Add '113.3333333' to each side of the equation. -113.3333333 + -2x + 113.3333333 + x2 = 0 + 113.3333333 Reorder the terms: -113.3333333 + 113.3333333 + -2x + x2 = 0 + 113.3333333 Combine like terms: -113.3333333 + 113.3333333 = 0.0000000 0.0000000 + -2x + x2 = 0 + 113.3333333 -2x + x2 = 0 + 113.3333333 Combine like terms: 0 + 113.3333333 = 113.3333333 -2x + x2 = 113.3333333 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 = 113.3333333 + 1 Reorder the terms: 1 + -2x + x2 = 113.3333333 + 1 Combine like terms: 113.3333333 + 1 = 114.3333333 1 + -2x + x2 = 114.3333333 Factor a perfect square on the left side: (x + -1)(x + -1) = 114.3333333 Calculate the square root of the right side: 10.69267662 Break this problem into two subproblems by setting (x + -1) equal to 10.69267662 and -10.69267662.Subproblem 1
x + -1 = 10.69267662 Simplifying x + -1 = 10.69267662 Reorder the terms: -1 + x = 10.69267662 Solving -1 + x = 10.69267662 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 = 10.69267662 + 1 Combine like terms: -1 + 1 = 0 0 + x = 10.69267662 + 1 x = 10.69267662 + 1 Combine like terms: 10.69267662 + 1 = 11.69267662 x = 11.69267662 Simplifying x = 11.69267662Subproblem 2
x + -1 = -10.69267662 Simplifying x + -1 = -10.69267662 Reorder the terms: -1 + x = -10.69267662 Solving -1 + x = -10.69267662 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 = -10.69267662 + 1 Combine like terms: -1 + 1 = 0 0 + x = -10.69267662 + 1 x = -10.69267662 + 1 Combine like terms: -10.69267662 + 1 = -9.69267662 x = -9.69267662 Simplifying x = -9.69267662Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.69267662, -9.69267662}
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