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Simplifying 0.6x2 + 294x + -0.03 = 0 Reorder the terms: -0.03 + 294x + 0.6x2 = 0 Solving -0.03 + 294x + 0.6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.6 the coefficient of the squared term: Divide each side by '0.6'. -0.05 + 490x + x2 = 0 Move the constant term to the right: Add '0.05' to each side of the equation. -0.05 + 490x + 0.05 + x2 = 0 + 0.05 Reorder the terms: -0.05 + 0.05 + 490x + x2 = 0 + 0.05 Combine like terms: -0.05 + 0.05 = 0.00 0.00 + 490x + x2 = 0 + 0.05 490x + x2 = 0 + 0.05 Combine like terms: 0 + 0.05 = 0.05 490x + x2 = 0.05 The x term is 490x. Take half its coefficient (245). Square it (60025) and add it to both sides. Add '60025' to each side of the equation. 490x + 60025 + x2 = 0.05 + 60025 Reorder the terms: 60025 + 490x + x2 = 0.05 + 60025 Combine like terms: 0.05 + 60025 = 60025.05 60025 + 490x + x2 = 60025.05 Factor a perfect square on the left side: (x + 245)(x + 245) = 60025.05 Calculate the square root of the right side: 245.000102041 Break this problem into two subproblems by setting (x + 245) equal to 245.000102041 and -245.000102041.Subproblem 1
x + 245 = 245.000102041 Simplifying x + 245 = 245.000102041 Reorder the terms: 245 + x = 245.000102041 Solving 245 + x = 245.000102041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-245' to each side of the equation. 245 + -245 + x = 245.000102041 + -245 Combine like terms: 245 + -245 = 0 0 + x = 245.000102041 + -245 x = 245.000102041 + -245 Combine like terms: 245.000102041 + -245 = 0.000102041 x = 0.000102041 Simplifying x = 0.000102041Subproblem 2
x + 245 = -245.000102041 Simplifying x + 245 = -245.000102041 Reorder the terms: 245 + x = -245.000102041 Solving 245 + x = -245.000102041 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-245' to each side of the equation. 245 + -245 + x = -245.000102041 + -245 Combine like terms: 245 + -245 = 0 0 + x = -245.000102041 + -245 x = -245.000102041 + -245 Combine like terms: -245.000102041 + -245 = -490.000102041 x = -490.000102041 Simplifying x = -490.000102041Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.000102041, -490.000102041}
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