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Simplifying 200 + 199.4x + -0.3x2 = 0 Solving 200 + 199.4x + -0.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -666.6666667 + -664.6666667x + x2 = 0 Move the constant term to the right: Add '666.6666667' to each side of the equation. -666.6666667 + -664.6666667x + 666.6666667 + x2 = 0 + 666.6666667 Reorder the terms: -666.6666667 + 666.6666667 + -664.6666667x + x2 = 0 + 666.6666667 Combine like terms: -666.6666667 + 666.6666667 = 0.0000000 0.0000000 + -664.6666667x + x2 = 0 + 666.6666667 -664.6666667x + x2 = 0 + 666.6666667 Combine like terms: 0 + 666.6666667 = 666.6666667 -664.6666667x + x2 = 666.6666667 The x term is -664.6666667x. Take half its coefficient (-332.3333334). Square it (110445.4445) and add it to both sides. Add '110445.4445' to each side of the equation. -664.6666667x + 110445.4445 + x2 = 666.6666667 + 110445.4445 Reorder the terms: 110445.4445 + -664.6666667x + x2 = 666.6666667 + 110445.4445 Combine like terms: 666.6666667 + 110445.4445 = 111112.1111667 110445.4445 + -664.6666667x + x2 = 111112.1111667 Factor a perfect square on the left side: (x + -332.3333334)(x + -332.3333334) = 111112.1111667 Calculate the square root of the right side: 333.334833413 Break this problem into two subproblems by setting (x + -332.3333334) equal to 333.334833413 and -333.334833413.Subproblem 1
x + -332.3333334 = 333.334833413 Simplifying x + -332.3333334 = 333.334833413 Reorder the terms: -332.3333334 + x = 333.334833413 Solving -332.3333334 + x = 333.334833413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '332.3333334' to each side of the equation. -332.3333334 + 332.3333334 + x = 333.334833413 + 332.3333334 Combine like terms: -332.3333334 + 332.3333334 = 0.0000000 0.0000000 + x = 333.334833413 + 332.3333334 x = 333.334833413 + 332.3333334 Combine like terms: 333.334833413 + 332.3333334 = 665.668166813 x = 665.668166813 Simplifying x = 665.668166813Subproblem 2
x + -332.3333334 = -333.334833413 Simplifying x + -332.3333334 = -333.334833413 Reorder the terms: -332.3333334 + x = -333.334833413 Solving -332.3333334 + x = -333.334833413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '332.3333334' to each side of the equation. -332.3333334 + 332.3333334 + x = -333.334833413 + 332.3333334 Combine like terms: -332.3333334 + 332.3333334 = 0.0000000 0.0000000 + x = -333.334833413 + 332.3333334 x = -333.334833413 + 332.3333334 Combine like terms: -333.334833413 + 332.3333334 = -1.001500013 x = -1.001500013 Simplifying x = -1.001500013Solution
The solution to the problem is based on the solutions from the subproblems. x = {665.668166813, -1.001500013}
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