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Simplifying 100x + -0.5x2 = 300 Solving 100x + -0.5x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + 100x + -0.5x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + 100x + -0.5x2 = 0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 600 + -200x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -200x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -200x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -200x + x2 = 0 + -600 -200x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -200x + x2 = -600 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 = -600 + 10000 Reorder the terms: 10000 + -200x + x2 = -600 + 10000 Combine like terms: -600 + 10000 = 9400 10000 + -200x + x2 = 9400 Factor a perfect square on the left side: (x + -100)(x + -100) = 9400 Calculate the square root of the right side: 96.953597148 Break this problem into two subproblems by setting (x + -100) equal to 96.953597148 and -96.953597148.Subproblem 1
x + -100 = 96.953597148 Simplifying x + -100 = 96.953597148 Reorder the terms: -100 + x = 96.953597148 Solving -100 + x = 96.953597148 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 = 96.953597148 + 100 Combine like terms: -100 + 100 = 0 0 + x = 96.953597148 + 100 x = 96.953597148 + 100 Combine like terms: 96.953597148 + 100 = 196.953597148 x = 196.953597148 Simplifying x = 196.953597148Subproblem 2
x + -100 = -96.953597148 Simplifying x + -100 = -96.953597148 Reorder the terms: -100 + x = -96.953597148 Solving -100 + x = -96.953597148 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 = -96.953597148 + 100 Combine like terms: -100 + 100 = 0 0 + x = -96.953597148 + 100 x = -96.953597148 + 100 Combine like terms: -96.953597148 + 100 = 3.046402852 x = 3.046402852 Simplifying x = 3.046402852Solution
The solution to the problem is based on the solutions from the subproblems. x = {196.953597148, 3.046402852}
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