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Simplifying 200x + -1x2 = 2100 Solving 200x + -1x2 = 2100 Solving for variable 'x'. Reorder the terms: -2100 + 200x + -1x2 = 2100 + -2100 Combine like terms: 2100 + -2100 = 0 -2100 + 200x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2100 + -200x + x2 = 0 Move the constant term to the right: Add '-2100' to each side of the equation. 2100 + -200x + -2100 + x2 = 0 + -2100 Reorder the terms: 2100 + -2100 + -200x + x2 = 0 + -2100 Combine like terms: 2100 + -2100 = 0 0 + -200x + x2 = 0 + -2100 -200x + x2 = 0 + -2100 Combine like terms: 0 + -2100 = -2100 -200x + x2 = -2100 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = -2100 + 10000 Reorder the terms: 10000 + -200x + x2 = -2100 + 10000 Combine like terms: -2100 + 10000 = 7900 10000 + -200x + x2 = 7900 Factor a perfect square on the left side: (x + -100)(x + -100) = 7900 Calculate the square root of the right side: 88.881944173 Break this problem into two subproblems by setting (x + -100) equal to 88.881944173 and -88.881944173.Subproblem 1
x + -100 = 88.881944173 Simplifying x + -100 = 88.881944173 Reorder the terms: -100 + x = 88.881944173 Solving -100 + x = 88.881944173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 88.881944173 + 100 Combine like terms: -100 + 100 = 0 0 + x = 88.881944173 + 100 x = 88.881944173 + 100 Combine like terms: 88.881944173 + 100 = 188.881944173 x = 188.881944173 Simplifying x = 188.881944173Subproblem 2
x + -100 = -88.881944173 Simplifying x + -100 = -88.881944173 Reorder the terms: -100 + x = -88.881944173 Solving -100 + x = -88.881944173 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -88.881944173 + 100 Combine like terms: -100 + 100 = 0 0 + x = -88.881944173 + 100 x = -88.881944173 + 100 Combine like terms: -88.881944173 + 100 = 11.118055827 x = 11.118055827 Simplifying x = 11.118055827Solution
The solution to the problem is based on the solutions from the subproblems. x = {188.881944173, 11.118055827}
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