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Simplifying 3x2 + x + -2(1000000000000) = 0 Multiply -2 * 1000000000000 3x2 + x + -2000000000000 = 0 Reorder the terms: -2000000000000 + x + 3x2 = 0 Solving -2000000000000 + x + 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'. -666666666700 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '666666666700' to each side of the equation. -666666666700 + 0.3333333333x + 666666666700 + x2 = 0 + 666666666700 Reorder the terms: -666666666700 + 666666666700 + 0.3333333333x + x2 = 0 + 666666666700 Combine like terms: -666666666700 + 666666666700 = 0 0 + 0.3333333333x + x2 = 0 + 666666666700 0.3333333333x + x2 = 0 + 666666666700 Combine like terms: 0 + 666666666700 = 666666666700 0.3333333333x + x2 = 666666666700 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.3333333333x + 0.25 + x2 = 666666666700 + 0.25 Reorder the terms: 0.25 + 0.3333333333x + x2 = 666666666700 + 0.25 Combine like terms: 666666666700 + 0.25 = 666666666700.25 0.25 + 0.3333333333x + x2 = 666666666700.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 666666666700.25 Calculate the square root of the right side: 816496.580948292 Break this problem into two subproblems by setting (x + 0.5) equal to 816496.580948292 and -816496.580948292.Subproblem 1
x + 0.5 = 816496.580948292 Simplifying x + 0.5 = 816496.580948292 Reorder the terms: 0.5 + x = 816496.580948292 Solving 0.5 + x = 816496.580948292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 816496.580948292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 816496.580948292 + -0.5 x = 816496.580948292 + -0.5 Combine like terms: 816496.580948292 + -0.5 = 816496.080948292 x = 816496.080948292 Simplifying x = 816496.080948292Subproblem 2
x + 0.5 = -816496.580948292 Simplifying x + 0.5 = -816496.580948292 Reorder the terms: 0.5 + x = -816496.580948292 Solving 0.5 + x = -816496.580948292 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -816496.580948292 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -816496.580948292 + -0.5 x = -816496.580948292 + -0.5 Combine like terms: -816496.580948292 + -0.5 = -816497.080948292 x = -816497.080948292 Simplifying x = -816497.080948292Solution
The solution to the problem is based on the solutions from the subproblems. x = {816496.080948292, -816497.080948292}
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