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Simplifying 0 = 0.02x2 + x + -100 Reorder the terms: 0 = -100 + x + 0.02x2 Solving 0 = -100 + x + 0.02x2 Solving for variable 'x'. Combine like terms: 0 + 100 = 100 100 + -1x + -0.02x2 = -100 + x + 0.02x2 + 100 + -1x + -0.02x2 Reorder the terms: 100 + -1x + -0.02x2 = -100 + 100 + x + -1x + 0.02x2 + -0.02x2 Combine like terms: -100 + 100 = 0 100 + -1x + -0.02x2 = 0 + x + -1x + 0.02x2 + -0.02x2 100 + -1x + -0.02x2 = x + -1x + 0.02x2 + -0.02x2 Combine like terms: x + -1x = 0 100 + -1x + -0.02x2 = 0 + 0.02x2 + -0.02x2 100 + -1x + -0.02x2 = 0.02x2 + -0.02x2 Combine like terms: 0.02x2 + -0.02x2 = 0.00 100 + -1x + -0.02x2 = 0.00 Begin completing the square. Divide all terms by -0.02 the coefficient of the squared term: Divide each side by '-0.02'. -5000 + 50x + x2 = 0 Move the constant term to the right: Add '5000' to each side of the equation. -5000 + 50x + 5000 + x2 = 0 + 5000 Reorder the terms: -5000 + 5000 + 50x + x2 = 0 + 5000 Combine like terms: -5000 + 5000 = 0 0 + 50x + x2 = 0 + 5000 50x + x2 = 0 + 5000 Combine like terms: 0 + 5000 = 5000 50x + x2 = 5000 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 5000 + 625 Reorder the terms: 625 + 50x + x2 = 5000 + 625 Combine like terms: 5000 + 625 = 5625 625 + 50x + x2 = 5625 Factor a perfect square on the left side: (x + 25)(x + 25) = 5625 Calculate the square root of the right side: 75 Break this problem into two subproblems by setting (x + 25) equal to 75 and -75.Subproblem 1
x + 25 = 75 Simplifying x + 25 = 75 Reorder the terms: 25 + x = 75 Solving 25 + x = 75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 75 + -25 Combine like terms: 25 + -25 = 0 0 + x = 75 + -25 x = 75 + -25 Combine like terms: 75 + -25 = 50 x = 50 Simplifying x = 50Subproblem 2
x + 25 = -75 Simplifying x + 25 = -75 Reorder the terms: 25 + x = -75 Solving 25 + x = -75 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -75 + -25 Combine like terms: 25 + -25 = 0 0 + x = -75 + -25 x = -75 + -25 Combine like terms: -75 + -25 = -100 x = -100 Simplifying x = -100Solution
The solution to the problem is based on the solutions from the subproblems. x = {50, -100}
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