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Simplifying 6x2 + -1x = 2000 Reorder the terms: -1x + 6x2 = 2000 Solving -1x + 6x2 = 2000 Solving for variable 'x'. Reorder the terms: -2000 + -1x + 6x2 = 2000 + -2000 Combine like terms: 2000 + -2000 = 0 -2000 + -1x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -333.3333333 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '333.3333333' to each side of the equation. -333.3333333 + -0.1666666667x + 333.3333333 + x2 = 0 + 333.3333333 Reorder the terms: -333.3333333 + 333.3333333 + -0.1666666667x + x2 = 0 + 333.3333333 Combine like terms: -333.3333333 + 333.3333333 = 0.0000000 0.0000000 + -0.1666666667x + x2 = 0 + 333.3333333 -0.1666666667x + x2 = 0 + 333.3333333 Combine like terms: 0 + 333.3333333 = 333.3333333 -0.1666666667x + x2 = 333.3333333 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 = 333.3333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 333.3333333 + 0.006944444447 Combine like terms: 333.3333333 + 0.006944444447 = 333.340277744447 0.006944444447 + -0.1666666667x + x2 = 333.340277744447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 333.340277744447 Calculate the square root of the right side: 18.257608763 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 18.257608763 and -18.257608763.Subproblem 1
x + -0.08333333335 = 18.257608763 Simplifying x + -0.08333333335 = 18.257608763 Reorder the terms: -0.08333333335 + x = 18.257608763 Solving -0.08333333335 + x = 18.257608763 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 = 18.257608763 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 18.257608763 + 0.08333333335 x = 18.257608763 + 0.08333333335 Combine like terms: 18.257608763 + 0.08333333335 = 18.34094209635 x = 18.34094209635 Simplifying x = 18.34094209635Subproblem 2
x + -0.08333333335 = -18.257608763 Simplifying x + -0.08333333335 = -18.257608763 Reorder the terms: -0.08333333335 + x = -18.257608763 Solving -0.08333333335 + x = -18.257608763 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 = -18.257608763 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -18.257608763 + 0.08333333335 x = -18.257608763 + 0.08333333335 Combine like terms: -18.257608763 + 0.08333333335 = -18.17427542965 x = -18.17427542965 Simplifying x = -18.17427542965Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.34094209635, -18.17427542965}
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