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Simplifying 6x2 + -1x + -960 = 0 Reorder the terms: -960 + -1x + 6x2 = 0 Solving -960 + -1x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -160 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + -0.1666666667x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + -0.1666666667x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + -0.1666666667x + x2 = 0 + 160 -0.1666666667x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 -0.1666666667x + x2 = 160 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 160 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 160 + 0.006944444447 Combine like terms: 160 + 0.006944444447 = 160.006944444447 0.006944444447 + -0.1666666667x + x2 = 160.006944444447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 160.006944444447 Calculate the square root of the right side: 12.649385141 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 12.649385141 and -12.649385141.Subproblem 1
x + -0.08333333335 = 12.649385141 Simplifying x + -0.08333333335 = 12.649385141 Reorder the terms: -0.08333333335 + x = 12.649385141 Solving -0.08333333335 + x = 12.649385141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 12.649385141 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 12.649385141 + 0.08333333335 x = 12.649385141 + 0.08333333335 Combine like terms: 12.649385141 + 0.08333333335 = 12.73271847435 x = 12.73271847435 Simplifying x = 12.73271847435Subproblem 2
x + -0.08333333335 = -12.649385141 Simplifying x + -0.08333333335 = -12.649385141 Reorder the terms: -0.08333333335 + x = -12.649385141 Solving -0.08333333335 + x = -12.649385141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -12.649385141 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -12.649385141 + 0.08333333335 x = -12.649385141 + 0.08333333335 Combine like terms: -12.649385141 + 0.08333333335 = -12.56605180765 x = -12.56605180765 Simplifying x = -12.56605180765Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.73271847435, -12.56605180765}
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