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Simplifying 2.3 + -0.03x + -0.0001x2 = 0 Solving 2.3 + -0.03x + -0.0001x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.0001 the coefficient of the squared term: Divide each side by '-0.0001'. -23000 + 300x + x2 = 0 Move the constant term to the right: Add '23000' to each side of the equation. -23000 + 300x + 23000 + x2 = 0 + 23000 Reorder the terms: -23000 + 23000 + 300x + x2 = 0 + 23000 Combine like terms: -23000 + 23000 = 0 0 + 300x + x2 = 0 + 23000 300x + x2 = 0 + 23000 Combine like terms: 0 + 23000 = 23000 300x + x2 = 23000 The x term is 300x. Take half its coefficient (150). Square it (22500) and add it to both sides. Add '22500' to each side of the equation. 300x + 22500 + x2 = 23000 + 22500 Reorder the terms: 22500 + 300x + x2 = 23000 + 22500 Combine like terms: 23000 + 22500 = 45500 22500 + 300x + x2 = 45500 Factor a perfect square on the left side: (x + 150)(x + 150) = 45500 Calculate the square root of the right side: 213.307290077 Break this problem into two subproblems by setting (x + 150) equal to 213.307290077 and -213.307290077.Subproblem 1
x + 150 = 213.307290077 Simplifying x + 150 = 213.307290077 Reorder the terms: 150 + x = 213.307290077 Solving 150 + x = 213.307290077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = 213.307290077 + -150 Combine like terms: 150 + -150 = 0 0 + x = 213.307290077 + -150 x = 213.307290077 + -150 Combine like terms: 213.307290077 + -150 = 63.307290077 x = 63.307290077 Simplifying x = 63.307290077Subproblem 2
x + 150 = -213.307290077 Simplifying x + 150 = -213.307290077 Reorder the terms: 150 + x = -213.307290077 Solving 150 + x = -213.307290077 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-150' to each side of the equation. 150 + -150 + x = -213.307290077 + -150 Combine like terms: 150 + -150 = 0 0 + x = -213.307290077 + -150 x = -213.307290077 + -150 Combine like terms: -213.307290077 + -150 = -363.307290077 x = -363.307290077 Simplifying x = -363.307290077Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.307290077, -363.307290077}
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