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Simplifying 0.5x2 + 100x + -5000 = 0 Reorder the terms: -5000 + 100x + 0.5x2 = 0 Solving -5000 + 100x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -10000 + 200x + x2 = 0 Move the constant term to the right: Add '10000' to each side of the equation. -10000 + 200x + 10000 + x2 = 0 + 10000 Reorder the terms: -10000 + 10000 + 200x + x2 = 0 + 10000 Combine like terms: -10000 + 10000 = 0 0 + 200x + x2 = 0 + 10000 200x + x2 = 0 + 10000 Combine like terms: 0 + 10000 = 10000 200x + x2 = 10000 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 = 10000 + 10000 Reorder the terms: 10000 + 200x + x2 = 10000 + 10000 Combine like terms: 10000 + 10000 = 20000 10000 + 200x + x2 = 20000 Factor a perfect square on the left side: (x + 100)(x + 100) = 20000 Calculate the square root of the right side: 141.421356237 Break this problem into two subproblems by setting (x + 100) equal to 141.421356237 and -141.421356237.Subproblem 1
x + 100 = 141.421356237 Simplifying x + 100 = 141.421356237 Reorder the terms: 100 + x = 141.421356237 Solving 100 + x = 141.421356237 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 = 141.421356237 + -100 Combine like terms: 100 + -100 = 0 0 + x = 141.421356237 + -100 x = 141.421356237 + -100 Combine like terms: 141.421356237 + -100 = 41.421356237 x = 41.421356237 Simplifying x = 41.421356237Subproblem 2
x + 100 = -141.421356237 Simplifying x + 100 = -141.421356237 Reorder the terms: 100 + x = -141.421356237 Solving 100 + x = -141.421356237 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 = -141.421356237 + -100 Combine like terms: 100 + -100 = 0 0 + x = -141.421356237 + -100 x = -141.421356237 + -100 Combine like terms: -141.421356237 + -100 = -241.421356237 x = -241.421356237 Simplifying x = -241.421356237Solution
The solution to the problem is based on the solutions from the subproblems. x = {41.421356237, -241.421356237}
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